TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2023
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/3355
AB  - The paper shows a way to create a set of tools that allows the construction of different models of spatial deltahedral structures as a result of the game. It is a set of accessories with which participants (school children, students) through play, experimenting with different layouts and combinations of elements of the whole, create spatial forms from uniform elements: sticks of length "a" and ringshaped joint connections. The game uses a STEM learning approach and the "learning by doing" method to provide knowledge about the spatial relationships of elements and static properties of the structure, in the process of playing. The process of forming structures via mentioned connecting elements uses the same principle of connecting supports and nodes as in the real space truss. A similar method is used by some other gaming platforms, such as Geomag, Magna-tiles, Picasso, or Blockaroo. Unlike them, our solution does not use magnets, but prestressing.
PB  - Faculty of Technical Sciences, University of Novi Sad
PB  - Serbian Society for Geometry and Graphics SUGIG
C3  - The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''
T1  - Learning while playing - Througie platform for creating models of spatial structures
EP  - 180
SP  - 169
UR  - https://hdl.handle.net/21.15107/rcub_grafar_3355
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2023",
abstract = "The paper shows a way to create a set of tools that allows the construction of different models of spatial deltahedral structures as a result of the game. It is a set of accessories with which participants (school children, students) through play, experimenting with different layouts and combinations of elements of the whole, create spatial forms from uniform elements: sticks of length "a" and ringshaped joint connections. The game uses a STEM learning approach and the "learning by doing" method to provide knowledge about the spatial relationships of elements and static properties of the structure, in the process of playing. The process of forming structures via mentioned connecting elements uses the same principle of connecting supports and nodes as in the real space truss. A similar method is used by some other gaming platforms, such as Geomag, Magna-tiles, Picasso, or Blockaroo. Unlike them, our solution does not use magnets, but prestressing.",
publisher = "Faculty of Technical Sciences, University of Novi Sad, Serbian Society for Geometry and Graphics SUGIG",
journal = "The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''",
title = "Learning while playing - Througie platform for creating models of spatial structures",
pages = "180-169",
url = "https://hdl.handle.net/21.15107/rcub_grafar_3355"
}

Obradović, M.,& Mišić, S.. (2023). Learning while playing - Througie platform for creating models of spatial structures. in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''
Faculty of Technical Sciences, University of Novi Sad., 169-180.
https://hdl.handle.net/21.15107/rcub_grafar_3355

Obradović M, Mišić S. Learning while playing - Througie platform for creating models of spatial structures. in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''. 2023;:169-180.
https://hdl.handle.net/21.15107/rcub_grafar_3355 .

Obradović, Marija, Mišić, Slobodan, "Learning while playing - Througie platform for creating models of spatial structures" in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023'' (2023):169-180,
https://hdl.handle.net/21.15107/rcub_grafar_3355 .

TY  - CONF
AU  - Obradović, Marija
AU  - Martinenko, Anastasija
PY  - 2023
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/3354
AB  - There are numerous ways to construct arches as curved structural elements that span openings in architectural buildings. Arches are present in many historical styles, having the role of an identification mark. Contemporary architecture also uses a resource of inherited styles, combining them into an eclectic blend of modern and classic. However, regardless of the aspirations that investors, architects and future users may have towards some of the complex stylistic forms, the question is whether every contractor will be able to meet the set requirements. Although modern construction technology is apt to
perform much more diverse forms than in earlier epochs, there are still situations when some problems, especially geometric ones, need to be solved, since the technology itself has not yet reached the point of its own thinking. One such problem was posed to the authors by a contractor who came up with the question: how to easily and accurately make a template for a semi-oval window arch, with a predefined point (M) through which the arch should pass. Hence, this is not about an elliptical arc for which there are a number of known constructions. The request was to offer a construction of a higher order curve, simple enough to enable quick and easy design and fabrication of templates on the construction site. In semi-oval arcs, the curve deviates from the elliptical one, giving greater curvature at the vertices of the major axis, and lesser at the vertex of the minor semi-axis. To solve this problem, we use the generalization of the Hügelschäffer’s egg curve construction. With input data: the major and minor semiaxes a and b, together with the given position of the point M which defines the deviation of the oval curve from the ellipse, we first determine the displacement of the minor circle of the Hügelschäffer’s construction along the y axis. Then, by applying the transformation of hyperbolism, we obtain the points of the semi-oval. The offered construction gives quick and accurate positions of points on the semi-oval arc, moreover, it allows the adjustment of the shape of the semi-oval arch according to needs (aesthetic, stylistic, constructive, functional, etc.). In the digital age, it is no problem to draw a higher order curve, but in order to simplify the construction for the purpose of making templates on the construction site, we can turn to the classic method - the approximation of curves with circles, as with semi-elliptical arcs. We find the centers of circles and use their successively connected arcs to accomplish the task with synthetic tools: compass and ruler.
PB  - Faculty of Technical Sciences, University of Novi Sad
PB  - Serbian Society for Geometry and Graphics SUGIG
C3  - The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''
T1  - A method for adjusting the shape of semi-oval arches using Hügelschäffer’s construction
EP  - 215
SP  - 205
UR  - https://hdl.handle.net/21.15107/rcub_grafar_3354
ER  - 

@conference{
author = "Obradović, Marija and Martinenko, Anastasija",
year = "2023",
abstract = "There are numerous ways to construct arches as curved structural elements that span openings in architectural buildings. Arches are present in many historical styles, having the role of an identification mark. Contemporary architecture also uses a resource of inherited styles, combining them into an eclectic blend of modern and classic. However, regardless of the aspirations that investors, architects and future users may have towards some of the complex stylistic forms, the question is whether every contractor will be able to meet the set requirements. Although modern construction technology is apt to
perform much more diverse forms than in earlier epochs, there are still situations when some problems, especially geometric ones, need to be solved, since the technology itself has not yet reached the point of its own thinking. One such problem was posed to the authors by a contractor who came up with the question: how to easily and accurately make a template for a semi-oval window arch, with a predefined point (M) through which the arch should pass. Hence, this is not about an elliptical arc for which there are a number of known constructions. The request was to offer a construction of a higher order curve, simple enough to enable quick and easy design and fabrication of templates on the construction site. In semi-oval arcs, the curve deviates from the elliptical one, giving greater curvature at the vertices of the major axis, and lesser at the vertex of the minor semi-axis. To solve this problem, we use the generalization of the Hügelschäffer’s egg curve construction. With input data: the major and minor semiaxes a and b, together with the given position of the point M which defines the deviation of the oval curve from the ellipse, we first determine the displacement of the minor circle of the Hügelschäffer’s construction along the y axis. Then, by applying the transformation of hyperbolism, we obtain the points of the semi-oval. The offered construction gives quick and accurate positions of points on the semi-oval arc, moreover, it allows the adjustment of the shape of the semi-oval arch according to needs (aesthetic, stylistic, constructive, functional, etc.). In the digital age, it is no problem to draw a higher order curve, but in order to simplify the construction for the purpose of making templates on the construction site, we can turn to the classic method - the approximation of curves with circles, as with semi-elliptical arcs. We find the centers of circles and use their successively connected arcs to accomplish the task with synthetic tools: compass and ruler.",
publisher = "Faculty of Technical Sciences, University of Novi Sad, Serbian Society for Geometry and Graphics SUGIG",
journal = "The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''",
title = "A method for adjusting the shape of semi-oval arches using Hügelschäffer’s construction",
pages = "215-205",
url = "https://hdl.handle.net/21.15107/rcub_grafar_3354"
}

Obradović, M.,& Martinenko, A.. (2023). A method for adjusting the shape of semi-oval arches using Hügelschäffer’s construction. in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''
Faculty of Technical Sciences, University of Novi Sad., 205-215.
https://hdl.handle.net/21.15107/rcub_grafar_3354

Obradović M, Martinenko A. A method for adjusting the shape of semi-oval arches using Hügelschäffer’s construction. in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023''. 2023;:205-215.
https://hdl.handle.net/21.15107/rcub_grafar_3354 .

Obradović, Marija, Martinenko, Anastasija, "A method for adjusting the shape of semi-oval arches using Hügelschäffer’s construction" in The 9th International Scientific Conference on Geometry and Graphics ''Mongeometrija 2023'' (2023):205-215,
https://hdl.handle.net/21.15107/rcub_grafar_3354 .

TY  - CHAP
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2022
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2779
AB  - The paper considers a type of radial pentagon-based tiling consisting of two shapes: triangle and rectangle. The ob tained solution has a spatial interpretation in a 3D arrangement of equilateral triangles and squares dictated by the particular array of concave cupolae of the second sort, minor type (CC-II 5.m). These cupolae are arranged so that their decagonal bases partly overlap, making a pentagonal pattern (similar to the one of the Penrose tiling). Covering the folds between the faces of such a polyhedral structure with polygons, we use exactly equi lateral triangles and squares, thanks to the trigonometric prop erties of CC-II-5.m. Observed in the orthogonal projection onto the plane of the polygonal bases, this 3D “covering” is viewed as a pentagonal-based radial tiling in the Euclidean plane. Equilateral triangles will be projected into congruent isosceles triangles corresponding to those obtained by the radial sec tion of a regular pentagon in 5 parts. The squares are project ed into rectangles whose ratio is: a:b = 1:φ/√(1+φ2), where φ 
is the golden ratio. These triangles and rectangles form a ra dial tiling consisting of 5 sectors of the plane, where the pat terns of the established tiles are repeated locally periodically. 
However, with 5-fold rotation of the pattern, the tiling itself is non-periodic. The various tiling solutions that can be obtained in this way may serve as inspiration for the geometric design, 
especially interesting in architecture and applied arts, e.g. for rosettes, brise soleils, mosaics, stained glass, fences, partition screens and the like
PB  - University of Arts in Belgrade, Faculty of Applied Arts, Kralja Petra 4, 11000 Belgrade, Serbia
T2  - Уметност и наука у примени: искуство и визија: Art and Science Applied: Experience and Vision
T1  - Pentagon-Based Radial Tiling with Triangles and Rectangles and Its Spatial Interpretation
EP  - 371
SP  - 353
VL  - 2
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2779
ER  - 

@inbook{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2022",
abstract = "The paper considers a type of radial pentagon-based tiling consisting of two shapes: triangle and rectangle. The ob tained solution has a spatial interpretation in a 3D arrangement of equilateral triangles and squares dictated by the particular array of concave cupolae of the second sort, minor type (CC-II 5.m). These cupolae are arranged so that their decagonal bases partly overlap, making a pentagonal pattern (similar to the one of the Penrose tiling). Covering the folds between the faces of such a polyhedral structure with polygons, we use exactly equi lateral triangles and squares, thanks to the trigonometric prop erties of CC-II-5.m. Observed in the orthogonal projection onto the plane of the polygonal bases, this 3D “covering” is viewed as a pentagonal-based radial tiling in the Euclidean plane. Equilateral triangles will be projected into congruent isosceles triangles corresponding to those obtained by the radial sec tion of a regular pentagon in 5 parts. The squares are project ed into rectangles whose ratio is: a:b = 1:φ/√(1+φ2), where φ 
is the golden ratio. These triangles and rectangles form a ra dial tiling consisting of 5 sectors of the plane, where the pat terns of the established tiles are repeated locally periodically. 
However, with 5-fold rotation of the pattern, the tiling itself is non-periodic. The various tiling solutions that can be obtained in this way may serve as inspiration for the geometric design, 
especially interesting in architecture and applied arts, e.g. for rosettes, brise soleils, mosaics, stained glass, fences, partition screens and the like",
publisher = "University of Arts in Belgrade, Faculty of Applied Arts, Kralja Petra 4, 11000 Belgrade, Serbia",
journal = "Уметност и наука у примени: искуство и визија: Art and Science Applied: Experience and Vision",
booktitle = "Pentagon-Based Radial Tiling with Triangles and Rectangles and Its Spatial Interpretation",
pages = "371-353",
volume = "2",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2779"
}

Obradović, M.,& Mišić, S.. (2022). Pentagon-Based Radial Tiling with Triangles and Rectangles and Its Spatial Interpretation. in Уметност и наука у примени: искуство и визија: Art and Science Applied: Experience and Vision
University of Arts in Belgrade, Faculty of Applied Arts, Kralja Petra 4, 11000 Belgrade, Serbia., 2, 353-371.
https://hdl.handle.net/21.15107/rcub_grafar_2779

Obradović M, Mišić S. Pentagon-Based Radial Tiling with Triangles and Rectangles and Its Spatial Interpretation. in Уметност и наука у примени: искуство и визија: Art and Science Applied: Experience and Vision. 2022;2:353-371.
https://hdl.handle.net/21.15107/rcub_grafar_2779 .

Obradović, Marija, Mišić, Slobodan, "Pentagon-Based Radial Tiling with Triangles and Rectangles and Its Spatial Interpretation" in Уметност и наука у примени: искуство и визија: Art and Science Applied: Experience and Vision, 2 (2022):353-371,
https://hdl.handle.net/21.15107/rcub_grafar_2779 .

TY  - CHAP
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2022
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2698
AB  - Finding a possibility to create unique polyhedral surfaces with such specific geometric regularities as the congruence of faces, a high level of symmetry and the ability to describe an infinite polyhedron, served as a starting point for the explorations in this study. Such surfaces can be obtained through a single element, the equilateral triangle, given that they are deltahedral. Here, we will focus on deltahedral rings composed of fragments of the concave antiprisms of the second sort, type major, that we identify as CA-II-n.M. This paper shows not only that it is possible to close a full ring using fragments of selected CA-II-n.M, but also that we can predict the shape of the ring depending on the number of sides of the base-polygon {n} within the chosen CA-II-n.M. The number of solutions obtained for each CA-II-n.M’s representative depends on n and can vary from 1 to 5, out of 8 possible solutions.
PB  - Birkhäuser, Cham, 2022
T2  - Polyhedra and Beyond
T1  - Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort
EP  - 68
SP  - 53
DO  - 10.1007/978-3-030-99116-6_4
ER  - 

@inbook{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2022",
abstract = "Finding a possibility to create unique polyhedral surfaces with such specific geometric regularities as the congruence of faces, a high level of symmetry and the ability to describe an infinite polyhedron, served as a starting point for the explorations in this study. Such surfaces can be obtained through a single element, the equilateral triangle, given that they are deltahedral. Here, we will focus on deltahedral rings composed of fragments of the concave antiprisms of the second sort, type major, that we identify as CA-II-n.M. This paper shows not only that it is possible to close a full ring using fragments of selected CA-II-n.M, but also that we can predict the shape of the ring depending on the number of sides of the base-polygon {n} within the chosen CA-II-n.M. The number of solutions obtained for each CA-II-n.M’s representative depends on n and can vary from 1 to 5, out of 8 possible solutions.",
publisher = "Birkhäuser, Cham, 2022",
journal = "Polyhedra and Beyond",
booktitle = "Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort",
pages = "68-53",
doi = "10.1007/978-3-030-99116-6_4"
}

Obradović, M.,& Mišić, S.. (2022). Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort. in Polyhedra and Beyond
Birkhäuser, Cham, 2022., 53-68.
https://doi.org/10.1007/978-3-030-99116-6_4

Obradović M, Mišić S. Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort. in Polyhedra and Beyond. 2022;:53-68.
doi:10.1007/978-3-030-99116-6_4 .

Obradović, Marija, Mišić, Slobodan, "Concave Deltahedral Rings Based on the Geometry of Concave Antiprisms of the Second Sort" in Polyhedra and Beyond (2022):53-68,
https://doi.org/10.1007/978-3-030-99116-6_4 . .

TY  - CONF
AU  - Martinenko, Anastasija
AU  - Obradović, Marija
PY  - 2021
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2527
AB  - The paper presents a way of visualizing terrain changes in the observed time period, caused by natural disasters such as landslide. The application of the Google Earth Pro application for generation of DSM (Digital Area Model) data is presented, and the software package Qgis with accompanying tools was used for analysis, modelling and visualization of the obtained data. The settlement of Umka in the city municipality of Čukarica in Belgrade was adopted as an area of interest. Part of Umka territory is a landslide, a geodynamic process which is considered a natural disaster. Thus, as such, it is interesting to monitor changes in the terrain over time period. Changes were monitored within intervals of 8 years, for a period of 2011 to 2019. In Google Earth Pro, DSM was generated via isohypses. Data were generated for different dates using Historical imagery option and compared over time. Obtaining DSM through isohypses in this manner is an efficient and cheap way to obtain terrain data. Therefore, despite certain inaccuracies compared to standard practice, it can be applied in cases where a high level of accuracy is not required, and it is necessary to prepare data in a short time. The method presented in this paper is suitable for a preliminary review of the condition of the terrain, without the need for more demanding procedures.
The processing of the generated DSM was performed with Qgis software application. For the selected area of interest, the DSM data was exported from Google Earth Pro and loaded into Qgis. By applying the existing tools, additional terrain analyzes of the area were performed. As a result, terrain models are presented, showing clearly visible changes that occurred within a given time period. The described procedure itself provides several important advantages compared to standard procedures: the use of freeware, rapidity of obtaining results, simultaneous visualization of changes, simplicity of the procedure and obtaining results accurate enough for immediate evaluation of the situation on site. In addition, due to its illustrative nature, this method can be used for educational purposes.
PB  - Serbian Society for Geometry and Graphics (SUGIG)
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - Proceedings of 8th International Scientific Conference “moNGeometrija 2021”
T1  - Visualization of geodynamic changes of terrain using Google Earth Pro and Qgis
EP  - 185
SP  - 178
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2527
ER  - 

@conference{
author = "Martinenko, Anastasija and Obradović, Marija",
year = "2021",
abstract = "The paper presents a way of visualizing terrain changes in the observed time period, caused by natural disasters such as landslide. The application of the Google Earth Pro application for generation of DSM (Digital Area Model) data is presented, and the software package Qgis with accompanying tools was used for analysis, modelling and visualization of the obtained data. The settlement of Umka in the city municipality of Čukarica in Belgrade was adopted as an area of interest. Part of Umka territory is a landslide, a geodynamic process which is considered a natural disaster. Thus, as such, it is interesting to monitor changes in the terrain over time period. Changes were monitored within intervals of 8 years, for a period of 2011 to 2019. In Google Earth Pro, DSM was generated via isohypses. Data were generated for different dates using Historical imagery option and compared over time. Obtaining DSM through isohypses in this manner is an efficient and cheap way to obtain terrain data. Therefore, despite certain inaccuracies compared to standard practice, it can be applied in cases where a high level of accuracy is not required, and it is necessary to prepare data in a short time. The method presented in this paper is suitable for a preliminary review of the condition of the terrain, without the need for more demanding procedures.
The processing of the generated DSM was performed with Qgis software application. For the selected area of interest, the DSM data was exported from Google Earth Pro and loaded into Qgis. By applying the existing tools, additional terrain analyzes of the area were performed. As a result, terrain models are presented, showing clearly visible changes that occurred within a given time period. The described procedure itself provides several important advantages compared to standard procedures: the use of freeware, rapidity of obtaining results, simultaneous visualization of changes, simplicity of the procedure and obtaining results accurate enough for immediate evaluation of the situation on site. In addition, due to its illustrative nature, this method can be used for educational purposes.",
publisher = "Serbian Society for Geometry and Graphics (SUGIG), Faculty of Mechanical Engineering, University of Belgrade",
journal = "Proceedings of 8th International Scientific Conference “moNGeometrija 2021”",
title = "Visualization of geodynamic changes of terrain using Google Earth Pro and Qgis",
pages = "185-178",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2527"
}

Martinenko, A.,& Obradović, M.. (2021). Visualization of geodynamic changes of terrain using Google Earth Pro and Qgis. in Proceedings of 8th International Scientific Conference “moNGeometrija 2021”
Serbian Society for Geometry and Graphics (SUGIG)., 178-185.
https://hdl.handle.net/21.15107/rcub_grafar_2527

Martinenko A, Obradović M. Visualization of geodynamic changes of terrain using Google Earth Pro and Qgis. in Proceedings of 8th International Scientific Conference “moNGeometrija 2021”. 2021;:178-185.
https://hdl.handle.net/21.15107/rcub_grafar_2527 .

Martinenko, Anastasija, Obradović, Marija, "Visualization of geodynamic changes of terrain using Google Earth Pro and Qgis" in Proceedings of 8th International Scientific Conference “moNGeometrija 2021” (2021):178-185,
https://hdl.handle.net/21.15107/rcub_grafar_2527 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2021
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2528
AB  - The paper considers a type of radial pentagon-based tiling consisted of two shapes: triangle
and rectangle. The obtained solution has a spatial interpretation in a 3D arrangement of
equilateral triangles and squares dictated by the particular array of concave cupolae of the
second sort, minor type (CC-II-5.m). These cupolae are arranged so that their decagonal
bases partly overlap, making a pentagonal pattern (similar to one of the Penrose tiling).
Covering the folds between the faces of such a polyhedral structure with polygons,we use
exactly equilateral triangles and squares, thanks to the trigonometric properties of CC-II-5.m.
Observed in the orthogonal projection onto the plane of the polygonal bases, this 3D “covering” is viewed as a pentagonal-based radial tiling in the Euclidean plane. Equilateral triangles
will be projected into congruent isosceles triangles corresponding to those obtained by the
radial section of a regular pentagon in 5 parts. The squares are projected into rectangles
whose ratio a:b = 1:φ/√(1+φ2), where φ is the golden ratio. These triangles and rectangles
form a radial tiling consisting of 5 sectors of the plane, where the established tiles’ patterns
are repeated locally periodically. However, with 5-fold rotation of the pattern, the tilling itself
is non-periodic. The various tiling solution that can be obtained in this way may serve as
inspiration for the geometric design, especially interesting in architecture and applied arts,
e.g. for rosettes, brise soleils, mosaics, stained glass, fences, partition screens and the like
PB  - Faculty of Applied Arts, University of Arts in Belgrade, Serbia
C3  - SmartArt | Књига апстраката| Book of Abstracts
T1  - Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation
SP  - 58
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2528
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2021",
abstract = "The paper considers a type of radial pentagon-based tiling consisted of two shapes: triangle
and rectangle. The obtained solution has a spatial interpretation in a 3D arrangement of
equilateral triangles and squares dictated by the particular array of concave cupolae of the
second sort, minor type (CC-II-5.m). These cupolae are arranged so that their decagonal
bases partly overlap, making a pentagonal pattern (similar to one of the Penrose tiling).
Covering the folds between the faces of such a polyhedral structure with polygons,we use
exactly equilateral triangles and squares, thanks to the trigonometric properties of CC-II-5.m.
Observed in the orthogonal projection onto the plane of the polygonal bases, this 3D “covering” is viewed as a pentagonal-based radial tiling in the Euclidean plane. Equilateral triangles
will be projected into congruent isosceles triangles corresponding to those obtained by the
radial section of a regular pentagon in 5 parts. The squares are projected into rectangles
whose ratio a:b = 1:φ/√(1+φ2), where φ is the golden ratio. These triangles and rectangles
form a radial tiling consisting of 5 sectors of the plane, where the established tiles’ patterns
are repeated locally periodically. However, with 5-fold rotation of the pattern, the tilling itself
is non-periodic. The various tiling solution that can be obtained in this way may serve as
inspiration for the geometric design, especially interesting in architecture and applied arts,
e.g. for rosettes, brise soleils, mosaics, stained glass, fences, partition screens and the like",
publisher = "Faculty of Applied Arts, University of Arts in Belgrade, Serbia",
journal = "SmartArt | Књига апстраката| Book of Abstracts",
title = "Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation",
pages = "58",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2528"
}

Obradović, M.,& Mišić, S.. (2021). Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation. in SmartArt | Књига апстраката| Book of Abstracts
Faculty of Applied Arts, University of Arts in Belgrade, Serbia., 58.
https://hdl.handle.net/21.15107/rcub_grafar_2528

Obradović M, Mišić S. Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation. in SmartArt | Књига апстраката| Book of Abstracts. 2021;:58.
https://hdl.handle.net/21.15107/rcub_grafar_2528 .

Obradović, Marija, Mišić, Slobodan, "Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation" in SmartArt | Књига апстраката| Book of Abstracts (2021):58,
https://hdl.handle.net/21.15107/rcub_grafar_2528 .

TY  - CONF
AU  - Obradović, Marija
PY  - 2021
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2526
AB  - This paper presents a gallery of tessellations created by combining the following equilateral shapes: diamonds and stars, which can be further assembled into a pineapple shape. These three shapes can be decomposed into simpler shapes: an isosceles triangle and a rectangle. The triangle is formed by a subdivision of the regular pentagon into five equal sections, so that each have a base of length 𝒂�� and legs of length 𝒃��. The rectangle is created by having the same 𝒂�� and 𝒃�� for its sides. The diamond is formed by two such triangles and one rectangle, while the star is formed by a radial arrangement of five triangles back into the pentagon onto which five more triangles are added (elevated). Using these two shapes, we can tile the Euclidean plane without overlaps and gaps in different ways, including the pentagonal matrix. They can be further assembled into a "pineapple" shape, which can also tile the plane arranged in different ways, using only one shape (tile). We present several examples that include: periodic, non-periodic, rotational, radial and free-form tessellations. These shapes, in addition to their visual attractiveness and decorativeness which can be used in design, also hide the connection with patterns that can be found in nature, similar to Turing patterns.
PB  - Serbian Society for Geometry and Graphics (SUGIG)
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - Proceedings of 8th International Scientific Conference “moNGeometrija 2021”
T1  - Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon
EP  - 142
SP  - 130
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2526
ER  - 

@conference{
author = "Obradović, Marija",
year = "2021",
abstract = "This paper presents a gallery of tessellations created by combining the following equilateral shapes: diamonds and stars, which can be further assembled into a pineapple shape. These three shapes can be decomposed into simpler shapes: an isosceles triangle and a rectangle. The triangle is formed by a subdivision of the regular pentagon into five equal sections, so that each have a base of length 𝒂�� and legs of length 𝒃��. The rectangle is created by having the same 𝒂�� and 𝒃�� for its sides. The diamond is formed by two such triangles and one rectangle, while the star is formed by a radial arrangement of five triangles back into the pentagon onto which five more triangles are added (elevated). Using these two shapes, we can tile the Euclidean plane without overlaps and gaps in different ways, including the pentagonal matrix. They can be further assembled into a "pineapple" shape, which can also tile the plane arranged in different ways, using only one shape (tile). We present several examples that include: periodic, non-periodic, rotational, radial and free-form tessellations. These shapes, in addition to their visual attractiveness and decorativeness which can be used in design, also hide the connection with patterns that can be found in nature, similar to Turing patterns.",
publisher = "Serbian Society for Geometry and Graphics (SUGIG), Faculty of Mechanical Engineering, University of Belgrade",
journal = "Proceedings of 8th International Scientific Conference “moNGeometrija 2021”",
title = "Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon",
pages = "142-130",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2526"
}

Obradović, M.. (2021). Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon. in Proceedings of 8th International Scientific Conference “moNGeometrija 2021”
Serbian Society for Geometry and Graphics (SUGIG)., 130-142.
https://hdl.handle.net/21.15107/rcub_grafar_2526

Obradović M. Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon. in Proceedings of 8th International Scientific Conference “moNGeometrija 2021”. 2021;:130-142.
https://hdl.handle.net/21.15107/rcub_grafar_2526 .

Obradović, Marija, "Tilings with diamond, star and pineapple shapes based on the geometry of the regular pentagon" in Proceedings of 8th International Scientific Conference “moNGeometrija 2021” (2021):130-142,
https://hdl.handle.net/21.15107/rcub_grafar_2526 .

TY  - CONF
AU  - Mišić, Slobodan
AU  - Obradović, Marija
AU  - Milakić, Mirjana
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2202
AB  - In this paper concave deltahedral surfaces are applied to link the two concepts of geometric rosette design – the polar distribution of the unit element (circular arc) around the center of the contour circle and the rosettes obtained by means of  regular polygons. Forming composite polyhedral structures based on the geometry of concave deltahedral surfaces over a n-sided polygonal base, we have demonstrated one possible method of geometrical generation of three-dimensional rosettes. The concave polyhedral surfaces are lateral surfaces of the concave polyhedrons of the second, fourth and higher sorts, consisting of series of equilateral triangles, grouped into spatial pentahedrons and hexahedrons. Positioned polarly around the central axis of the regular polygon in the polyhedron’s basis and linked by triangles, the spatial pentahedrons and hexahedrons form the deltahedral surface. The sort of the concave polyhedron is determined by the number of equilateral triangle rows in thus obtained polyhedron’s net. In this study, composite polyhedral structures whose surface areas form the three-dimensional rosette are obtained through the combination of concave cupolae of the second sort (CC-II), concave cupolae of the fourth sort (CC-IV), concave antiprisms of the second sort (CA-II) and concave pyramids (CP). By means of elongation, gyro-elongation and augmentation of the listed concave polyhedrons it was possible to generate complex polyhedral structures, which can be used to create three-dimensional rosettes. The parameters of the solids were determined constructively by geometric methods and analytical methods which useiterative numericalprocedures.
PB  - Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020
C3  - ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIEDFrom Inspiration to Interaction
T1  - Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces
EP  - 422
SP  - 410
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2202
ER  - 

@conference{
author = "Mišić, Slobodan and Obradović, Marija and Milakić, Mirjana",
year = "2020",
abstract = "In this paper concave deltahedral surfaces are applied to link the two concepts of geometric rosette design – the polar distribution of the unit element (circular arc) around the center of the contour circle and the rosettes obtained by means of  regular polygons. Forming composite polyhedral structures based on the geometry of concave deltahedral surfaces over a n-sided polygonal base, we have demonstrated one possible method of geometrical generation of three-dimensional rosettes. The concave polyhedral surfaces are lateral surfaces of the concave polyhedrons of the second, fourth and higher sorts, consisting of series of equilateral triangles, grouped into spatial pentahedrons and hexahedrons. Positioned polarly around the central axis of the regular polygon in the polyhedron’s basis and linked by triangles, the spatial pentahedrons and hexahedrons form the deltahedral surface. The sort of the concave polyhedron is determined by the number of equilateral triangle rows in thus obtained polyhedron’s net. In this study, composite polyhedral structures whose surface areas form the three-dimensional rosette are obtained through the combination of concave cupolae of the second sort (CC-II), concave cupolae of the fourth sort (CC-IV), concave antiprisms of the second sort (CA-II) and concave pyramids (CP). By means of elongation, gyro-elongation and augmentation of the listed concave polyhedrons it was possible to generate complex polyhedral structures, which can be used to create three-dimensional rosettes. The parameters of the solids were determined constructively by geometric methods and analytical methods which useiterative numericalprocedures.",
publisher = "Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020",
journal = "ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIEDFrom Inspiration to Interaction",
title = "Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces",
pages = "422-410",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2202"
}

Mišić, S., Obradović, M.,& Milakić, M.. (2020). Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces. in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIEDFrom Inspiration to Interaction
Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020., 410-422.
https://hdl.handle.net/21.15107/rcub_grafar_2202

Mišić S, Obradović M, Milakić M. Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces. in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIEDFrom Inspiration to Interaction. 2020;:410-422.
https://hdl.handle.net/21.15107/rcub_grafar_2202 .

Mišić, Slobodan, Obradović, Marija, Milakić, Mirjana, "Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces" in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIEDFrom Inspiration to Interaction (2020):410-422,
https://hdl.handle.net/21.15107/rcub_grafar_2202 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2203
AB  - Using the concave polyhedra of the second sort, we are creating spatial structures in the shape of lattice panels to be applied in architecture. The procedure is based on a rectangular (or, less often, a polar) array of identical representatives of the concave polyhedra that include: concave antiprisms, concave cupolae and concave pyramids of the second sort. The selected representative, as a unit cell, can be arrayed so to touch the adjacent cells by vertex, by edge or by face. Thereby, they are  forming 3D lattice, similar to the 2D lattices patterns. We are using a single layer of these structures to form a shape most convenient for architectural usage, which is a shape of a panel. These 3D lattice panels are proposed to be used as brise-soleil, room dividers, fences, etc. The additional layer of visual design when using such a panels is accomplished with the shadows they cast, depending on the time and day of the year. 3D shape emphasizes the play of light and shadow, so these lattice panels can have a significant role as an element of decoration, i.e. architectural ornament.
PB  - Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020
C3  - ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIED From Inspiration to Interaction
T1  - 3D Lattice Panels Based on the Concave Polyhedra of the Second Sort: Ideas for Architectural Ornaments
EP  - 409
SP  - 394
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2203
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2020",
abstract = "Using the concave polyhedra of the second sort, we are creating spatial structures in the shape of lattice panels to be applied in architecture. The procedure is based on a rectangular (or, less often, a polar) array of identical representatives of the concave polyhedra that include: concave antiprisms, concave cupolae and concave pyramids of the second sort. The selected representative, as a unit cell, can be arrayed so to touch the adjacent cells by vertex, by edge or by face. Thereby, they are  forming 3D lattice, similar to the 2D lattices patterns. We are using a single layer of these structures to form a shape most convenient for architectural usage, which is a shape of a panel. These 3D lattice panels are proposed to be used as brise-soleil, room dividers, fences, etc. The additional layer of visual design when using such a panels is accomplished with the shadows they cast, depending on the time and day of the year. 3D shape emphasizes the play of light and shadow, so these lattice panels can have a significant role as an element of decoration, i.e. architectural ornament.",
publisher = "Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020",
journal = "ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIED From Inspiration to Interaction",
title = "3D Lattice Panels Based on the Concave Polyhedra of the Second Sort: Ideas for Architectural Ornaments",
pages = "409-394",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2203"
}

Obradović, M.,& Mišić, S.. (2020). 3D Lattice Panels Based on the Concave Polyhedra of the Second Sort: Ideas for Architectural Ornaments. in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIED From Inspiration to Interaction
Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020., 394-409.
https://hdl.handle.net/21.15107/rcub_grafar_2203

Obradović M, Mišić S. 3D Lattice Panels Based on the Concave Polyhedra of the Second Sort: Ideas for Architectural Ornaments. in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIED From Inspiration to Interaction. 2020;:394-409.
https://hdl.handle.net/21.15107/rcub_grafar_2203 .

Obradović, Marija, Mišić, Slobodan, "3D Lattice Panels Based on the Concave Polyhedra of the Second Sort: Ideas for Architectural Ornaments" in ЗБОРНИК РАДОВА: ПРВА МЕЂУНАРОДНА КОНФЕРЕНЦИЈА SMARTART – УМЕТНОСТ И НАУКА У ПРИМЕНИОд инспирације до интеракције / PROCEEDINGS: FIRST INTERNATIONAL CONFERENCE SMARTART – ART AND SCIENCE APPLIED From Inspiration to Interaction (2020):394-409,
https://hdl.handle.net/21.15107/rcub_grafar_2203 .

TY  - GEN
AU  - Obradović, Marija
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2204
AB  - Concave polyhedra of the second sort are a common name for polyhedra whose lateral surface is deltahedral, composed of a double row of equilateral triangles arranged in a 2π polar array over a regular polygonal base. Using representatives with an octagonal base, which have the greatest potential for modular fitting, we assemble complex shapes that can be applied as design solutions to architectural details. The column capitals are formed by a combination of the lateral deltahedral surfaces of the flower antiprisms (FA-II-8m), which serve as the backbone of the whole composition, concave antiprisms (CA-II-8M) and concave pyramids (CP-II-8m) of the second sort. By different arrangement of these elements, as well as by using different materials and colors, various ornate solutions can be obtained. Some of them are presented as suggested solutions. By combining different techniques of finishing the triangular faces of these deltahedral surfaces, whether in different materials, colors or in patterns obtained by face subdivisions, various decorative effects can be achieved, which can further enrich the appearance of both the capitals and the columns themselves.
PB  - Faculty of Mechanical Engineering, University of Belgrade
T2  - Dimensions reflected - catalog
T1  - Deltahedral Column Capitals
SP  - 12
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2204
ER  - 

@misc{
author = "Obradović, Marija",
year = "2020",
abstract = "Concave polyhedra of the second sort are a common name for polyhedra whose lateral surface is deltahedral, composed of a double row of equilateral triangles arranged in a 2π polar array over a regular polygonal base. Using representatives with an octagonal base, which have the greatest potential for modular fitting, we assemble complex shapes that can be applied as design solutions to architectural details. The column capitals are formed by a combination of the lateral deltahedral surfaces of the flower antiprisms (FA-II-8m), which serve as the backbone of the whole composition, concave antiprisms (CA-II-8M) and concave pyramids (CP-II-8m) of the second sort. By different arrangement of these elements, as well as by using different materials and colors, various ornate solutions can be obtained. Some of them are presented as suggested solutions. By combining different techniques of finishing the triangular faces of these deltahedral surfaces, whether in different materials, colors or in patterns obtained by face subdivisions, various decorative effects can be achieved, which can further enrich the appearance of both the capitals and the columns themselves.",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "Dimensions reflected - catalog",
title = "Deltahedral Column Capitals",
pages = "12",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2204"
}

Obradović, M.. (2020). Deltahedral Column Capitals. in Dimensions reflected - catalog
Faculty of Mechanical Engineering, University of Belgrade., 12.
https://hdl.handle.net/21.15107/rcub_grafar_2204

Obradović M. Deltahedral Column Capitals. in Dimensions reflected - catalog. 2020;:12.
https://hdl.handle.net/21.15107/rcub_grafar_2204 .

Obradović, Marija, "Deltahedral Column Capitals" in Dimensions reflected - catalog (2020):12,
https://hdl.handle.net/21.15107/rcub_grafar_2204 .

TY  - GEN
AU  - Obradović, Marija
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2205
AB  - The 7th International Conference MoNGgeometrija 2020 is organized and supported by Serbian Society for Geometry and Graphics (SUGIG) and the Faculty of Mechanical Engineering, University of Belgrade. Since SUGIG considers geometry and graphics to be the universal languages of science, technics and all visual arts, the conference offers the wide range of topics
which found their expression through the special Exhibition of ideas, designs and models under the name “Dimensions Reflected.” The Exhibition discloses and emphasizes the inspiring and fruitful influence of geometry on art, and at the same time the correlation between scientific exactness and poetics of visual arts. This Exhibition assures us that geometry is not only the
seed and the core of many different branches of science and techniques, but also the root of aesthetic postulates, clearly recognizable in the works of artists, architects, and designers. Despite the fact that geometry is a primeval knowledge and wisdom, its power does not fade or vanish through the time, but increases its strength and authority through contemporary arts and crafts. Thus, the Exhibition exposes and confirms the importance of geometric comprehension
through contributions in various scientific, engineering, and artistic fields, as well as through enhancing this precious base by means of modern digital techniques and technologies.
PB  - Faculty of Mechanical Engineering, University of Belgrade
T2  - Dimensions reflected - catalog
T1  - Dimensions reflected - catalog
EP  - 40
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2205
ER  - 

@misc{
author = "Obradović, Marija",
year = "2020",
abstract = "The 7th International Conference MoNGgeometrija 2020 is organized and supported by Serbian Society for Geometry and Graphics (SUGIG) and the Faculty of Mechanical Engineering, University of Belgrade. Since SUGIG considers geometry and graphics to be the universal languages of science, technics and all visual arts, the conference offers the wide range of topics
which found their expression through the special Exhibition of ideas, designs and models under the name “Dimensions Reflected.” The Exhibition discloses and emphasizes the inspiring and fruitful influence of geometry on art, and at the same time the correlation between scientific exactness and poetics of visual arts. This Exhibition assures us that geometry is not only the
seed and the core of many different branches of science and techniques, but also the root of aesthetic postulates, clearly recognizable in the works of artists, architects, and designers. Despite the fact that geometry is a primeval knowledge and wisdom, its power does not fade or vanish through the time, but increases its strength and authority through contemporary arts and crafts. Thus, the Exhibition exposes and confirms the importance of geometric comprehension
through contributions in various scientific, engineering, and artistic fields, as well as through enhancing this precious base by means of modern digital techniques and technologies.",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "Dimensions reflected - catalog",
title = "Dimensions reflected - catalog",
pages = "40-1",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2205"
}

Obradović, M.. (2020). Dimensions reflected - catalog. in Dimensions reflected - catalog
Faculty of Mechanical Engineering, University of Belgrade., 1-40.
https://hdl.handle.net/21.15107/rcub_grafar_2205

Obradović M. Dimensions reflected - catalog. in Dimensions reflected - catalog. 2020;:1-40.
https://hdl.handle.net/21.15107/rcub_grafar_2205 .

Obradović, Marija, "Dimensions reflected - catalog" in Dimensions reflected - catalog (2020):1-40,
https://hdl.handle.net/21.15107/rcub_grafar_2205 .

TY  - CONF
AU  - Obradović, Marija
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2206
AB  - This study presents a continuation of the research on the concave polyhedra of the second sort, adding to this family a new group of related polyhedra. They are formed over a specific type of isotoxal concave polygons that allow geometric arrangement of a double row of equilateral triangles into formations which enclose a deltahedral lateral surface without overlaps and gaps. As in all other representatives of the concave polyhedra of the second sort, we expect to find here the "major" and "minor" type, depending on the way we fold the net. This research has identified both these polyhedra types, which have the same planar net, but are formed over different basic concave polygons. The origination, constructive methods and properties of these solids are elaborated in the paper.
PB  - Belgrade: Serbian Society for Geometry and Graphics (SUGIG); Faculty of Mechanical Engineering, University of Belgrade
C3  - PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020
T1  - Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort
EP  - 26
SP  - 13
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2206
ER  - 

@conference{
author = "Obradović, Marija",
year = "2020",
abstract = "This study presents a continuation of the research on the concave polyhedra of the second sort, adding to this family a new group of related polyhedra. They are formed over a specific type of isotoxal concave polygons that allow geometric arrangement of a double row of equilateral triangles into formations which enclose a deltahedral lateral surface without overlaps and gaps. As in all other representatives of the concave polyhedra of the second sort, we expect to find here the "major" and "minor" type, depending on the way we fold the net. This research has identified both these polyhedra types, which have the same planar net, but are formed over different basic concave polygons. The origination, constructive methods and properties of these solids are elaborated in the paper.",
publisher = "Belgrade: Serbian Society for Geometry and Graphics (SUGIG); Faculty of Mechanical Engineering, University of Belgrade",
journal = "PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020",
title = "Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort",
pages = "26-13",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2206"
}

Obradović, M.. (2020). Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort. in PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020
Belgrade: Serbian Society for Geometry and Graphics (SUGIG); Faculty of Mechanical Engineering, University of Belgrade., 13-26.
https://hdl.handle.net/21.15107/rcub_grafar_2206

Obradović M. Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort. in PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020. 2020;:13-26.
https://hdl.handle.net/21.15107/rcub_grafar_2206 .

Obradović, Marija, "Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort" in PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020 (2020):13-26,
https://hdl.handle.net/21.15107/rcub_grafar_2206 .

TY  - CONF
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1945
AB  - The concave polyhedral surface of CC II can be used as a structural template for architectural design of domes, roofs or other covering or stand-alone structures. Subdivision of CC II faces in geometrically defined way can be observed as a part of the design process, if done with the intention to contribute to the aesthetic quality of the building itself. In this paper we discuss certain interventions on the tiled triangular faces of the CC II by regular triangles and hexagons, in order to get patterns applicable in architecture. By using different colors and / or materials of the tiles, we can get solutions that add the decorative layer to the structural one. Examining various solutions, this research focused on the D subdivision of the lateral polyhedral triangle (LPT) and in the resulting uniform tilings, searching for the ways to overcome monotony of highly symmetrical patterns. As opposed to exploring the ways of assembling the tiled LPTs with assigned layouts of tiles into shape of the CC II in order to get desired patterns on its surface, this paper explores the creation of various patterns within the existing, formerly obtained uniform tilings (2-uniform, trihexagonal tiling). A couple of conceptual solutions are given, as an illustration of the idea.
PB  - Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS
C3  - Journal of Industrial Design and Engineering Graphics (JIDEG)
T1  - Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture
EP  - 84
IS  - 1
SP  - 79
VL  - 14
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1945
ER  - 

@conference{
author = "Obradović, Marija",
year = "2019",
abstract = "The concave polyhedral surface of CC II can be used as a structural template for architectural design of domes, roofs or other covering or stand-alone structures. Subdivision of CC II faces in geometrically defined way can be observed as a part of the design process, if done with the intention to contribute to the aesthetic quality of the building itself. In this paper we discuss certain interventions on the tiled triangular faces of the CC II by regular triangles and hexagons, in order to get patterns applicable in architecture. By using different colors and / or materials of the tiles, we can get solutions that add the decorative layer to the structural one. Examining various solutions, this research focused on the D subdivision of the lateral polyhedral triangle (LPT) and in the resulting uniform tilings, searching for the ways to overcome monotony of highly symmetrical patterns. As opposed to exploring the ways of assembling the tiled LPTs with assigned layouts of tiles into shape of the CC II in order to get desired patterns on its surface, this paper explores the creation of various patterns within the existing, formerly obtained uniform tilings (2-uniform, trihexagonal tiling). A couple of conceptual solutions are given, as an illustration of the idea.",
publisher = "Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS",
journal = "Journal of Industrial Design and Engineering Graphics (JIDEG)",
title = "Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture",
pages = "84-79",
number = "1",
volume = "14",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1945"
}

Obradović, M.. (2019). Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture. in Journal of Industrial Design and Engineering Graphics (JIDEG)
Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS., 14(1), 79-84.
https://hdl.handle.net/21.15107/rcub_grafar_1945

Obradović M. Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture. in Journal of Industrial Design and Engineering Graphics (JIDEG). 2019;14(1):79-84.
https://hdl.handle.net/21.15107/rcub_grafar_1945 .

Obradović, Marija, "Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture" in Journal of Industrial Design and Engineering Graphics (JIDEG), 14, no. 1 (2019):79-84,
https://hdl.handle.net/21.15107/rcub_grafar_1945 .

TY  - CONF
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1944
AB  - The aim of this research is to examine and outline modularity of the selected representatives of concave pol yhedra of the second sort (C II), from the point of view of their high combinatorial potential for creating diverse polyhedral structures, some of which can be applied
in architectural design. The modularity is primarily attributed to the regular pol ygonal bases around which the solids are created. There are three basic groups of concave pol yhedra of the second sort: concave cupolae (CC II), concave pyramids (CP II) and concave antiprisms (CA.II). Since each of these groups contains the representatives with octagonal bases, they are chosen for this research, not only because of their compatibility, but also because of their accordance with the orthogonal matrix underlying the conventional modular grid, ubiquitous in architectural design. In this study, we examine the possibilities of modular conjoining of these
pol yhedra into new, composite structures, creating forms that can contribute to enrichment of architectural design expression, allowing easy execution at the same time.
PB  - Cham: Springer
C3  - Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics
T1  - Modularity of concave polyhedra of the second sort with octagonal bases
EP  - 954
SP  - 942
VL  - 809
DO  - 10.1007/978-3-319-95588-9_81
ER  - 

@conference{
author = "Obradović, Marija",
year = "2019",
abstract = "The aim of this research is to examine and outline modularity of the selected representatives of concave pol yhedra of the second sort (C II), from the point of view of their high combinatorial potential for creating diverse polyhedral structures, some of which can be applied
in architectural design. The modularity is primarily attributed to the regular pol ygonal bases around which the solids are created. There are three basic groups of concave pol yhedra of the second sort: concave cupolae (CC II), concave pyramids (CP II) and concave antiprisms (CA.II). Since each of these groups contains the representatives with octagonal bases, they are chosen for this research, not only because of their compatibility, but also because of their accordance with the orthogonal matrix underlying the conventional modular grid, ubiquitous in architectural design. In this study, we examine the possibilities of modular conjoining of these
pol yhedra into new, composite structures, creating forms that can contribute to enrichment of architectural design expression, allowing easy execution at the same time.",
publisher = "Cham: Springer",
journal = "Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics",
title = "Modularity of concave polyhedra of the second sort with octagonal bases",
pages = "954-942",
volume = "809",
doi = "10.1007/978-3-319-95588-9_81"
}

Obradović, M.. (2019). Modularity of concave polyhedra of the second sort with octagonal bases. in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics
Cham: Springer., 809, 942-954.
https://doi.org/10.1007/978-3-319-95588-9_81

Obradović M. Modularity of concave polyhedra of the second sort with octagonal bases. in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. 2019;809:942-954.
doi:10.1007/978-3-319-95588-9_81 .

Obradović, Marija, "Modularity of concave polyhedra of the second sort with octagonal bases" in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics, 809 (2019):942-954,
https://doi.org/10.1007/978-3-319-95588-9_81 . .

TY  - JOUR
AU  - Marković, Srđan
AU  - Obradović, Marija
AU  - Demetriades, Alexandros
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1004
AB  - We are facing a number of applications for altering portrait photographs using the help of artificial intelligence. Apart from the entertainment purposes, modern computer technologies can also help us get dynamic effects from static images, an example of which is the subject of this study. Dealing with the change of lighting in portraits photographs through real-time rendering, this paper provides a method of obtaining an image with variable light source that affects the facial features generated on the basis of the face tracking data acquired from the existing static photograph. Thus, we get a portrait with altered light, as if such a source was present at the actual moment of photographing. This method aims to improve or even change the visual experience when viewing the image, so that its further application corresponds to the given context.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Interactive change of lighting in the portrait images
EP  - 330
IS  - 2
SP  - 326
VL  - 47
DO  - 10.5937/fmet1902326M
ER  - 

@article{
author = "Marković, Srđan and Obradović, Marija and Demetriades, Alexandros",
year = "2019",
abstract = "We are facing a number of applications for altering portrait photographs using the help of artificial intelligence. Apart from the entertainment purposes, modern computer technologies can also help us get dynamic effects from static images, an example of which is the subject of this study. Dealing with the change of lighting in portraits photographs through real-time rendering, this paper provides a method of obtaining an image with variable light source that affects the facial features generated on the basis of the face tracking data acquired from the existing static photograph. Thus, we get a portrait with altered light, as if such a source was present at the actual moment of photographing. This method aims to improve or even change the visual experience when viewing the image, so that its further application corresponds to the given context.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Interactive change of lighting in the portrait images",
pages = "330-326",
number = "2",
volume = "47",
doi = "10.5937/fmet1902326M"
}

Marković, S., Obradović, M.,& Demetriades, A.. (2019). Interactive change of lighting in the portrait images. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 47(2), 326-330.
https://doi.org/10.5937/fmet1902326M

Marković S, Obradović M, Demetriades A. Interactive change of lighting in the portrait images. in FME Transactions. 2019;47(2):326-330.
doi:10.5937/fmet1902326M .

Marković, Srđan, Obradović, Marija, Demetriades, Alexandros, "Interactive change of lighting in the portrait images" in FME Transactions, 47, no. 2 (2019):326-330,
https://doi.org/10.5937/fmet1902326M . .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1981
AB  - Concave polyhedra of the second sort (abbreviated: C-II-n) constitute a group of polyhedra formed over regular n-sided base polygons and having a deltahedral lateral surfaces. This group includes: concave cupolae, concave pyramids and concave antiprisms of the second sort (CC-II-n, CP-II-n and CA-II-n, respectively). The common feature of these solids is that their lateral surfaces consist of a double row of equilateral triangles which can be assembled in two ways, making two different solids’ heights: major (C-II-nM) and minor (C-II-nm). The geometrical regularities and a high level of symmetry that characterizes these polyhedra, makes them suitable for joining and combining, so they can be arrayed infinitely in space, in x, y and z direction forming 3D lattice structures. For some representatives of these solids, the congruity of their lateral deltahedral surfaces occurs, so 3D tessellations are formed. 
In this paper, we focus on a single "layer" of such a structure, a panel-like 3D lattice. It is generated by multiplication of the chosen unit cell – the selected C-II-n representative – along the x-y directions. In the z direction the lateral surfaces form a deltahedral structure which makes the thickness of the panel. 
The method we used is based on the continuous connection of the edges of the two adjacent units, by joining relevant vertices. When we remove the base polygons, the unit cells become hollow, so they can create a honeycombed structure, more desirable for the purpose of application. Then, observed in 2D, by applying symmetry transformations, we form patterns similarly to the formation of wallpaper groups. In this way, we get visually interesting patterns in 2D, which transform into 3D lattice depending on the viewing angle. 
The thickness of the panel can be halved in some cases, so we get a thinner structure with "face" and "back", having different tessellations of polygons appearing on them. As an artistic intervention, these panels can be modified by joining deltahedral surfaces of other C-II-n onto the compatible faces, whereby we add another layer of patterns to the resulting structure. 
3D patterns and lattices are currently experiencing real boom in the design and industry, thanks to the 3D printing capabilities. As for architecture, they can be applied not only as an element of ornamentation, but also as a functional component of the project, especially concerning climate responsive facades.   
Due to the simplicity of the geometry of C-II-n, such 3D structures are feasible and easy to perform in terms of production and assembly. They are achievable not only with 3D printing, but can also be manually assembled or folded like origami, which allows the use of a much wider range of materials.
PB  - Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija
C3  - Smart Art Knjiga apstrakata / Book of abstracts
T1  - 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments
EP  - 88
SP  - 87
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1981
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2019",
abstract = "Concave polyhedra of the second sort (abbreviated: C-II-n) constitute a group of polyhedra formed over regular n-sided base polygons and having a deltahedral lateral surfaces. This group includes: concave cupolae, concave pyramids and concave antiprisms of the second sort (CC-II-n, CP-II-n and CA-II-n, respectively). The common feature of these solids is that their lateral surfaces consist of a double row of equilateral triangles which can be assembled in two ways, making two different solids’ heights: major (C-II-nM) and minor (C-II-nm). The geometrical regularities and a high level of symmetry that characterizes these polyhedra, makes them suitable for joining and combining, so they can be arrayed infinitely in space, in x, y and z direction forming 3D lattice structures. For some representatives of these solids, the congruity of their lateral deltahedral surfaces occurs, so 3D tessellations are formed. 
In this paper, we focus on a single "layer" of such a structure, a panel-like 3D lattice. It is generated by multiplication of the chosen unit cell – the selected C-II-n representative – along the x-y directions. In the z direction the lateral surfaces form a deltahedral structure which makes the thickness of the panel. 
The method we used is based on the continuous connection of the edges of the two adjacent units, by joining relevant vertices. When we remove the base polygons, the unit cells become hollow, so they can create a honeycombed structure, more desirable for the purpose of application. Then, observed in 2D, by applying symmetry transformations, we form patterns similarly to the formation of wallpaper groups. In this way, we get visually interesting patterns in 2D, which transform into 3D lattice depending on the viewing angle. 
The thickness of the panel can be halved in some cases, so we get a thinner structure with "face" and "back", having different tessellations of polygons appearing on them. As an artistic intervention, these panels can be modified by joining deltahedral surfaces of other C-II-n onto the compatible faces, whereby we add another layer of patterns to the resulting structure. 
3D patterns and lattices are currently experiencing real boom in the design and industry, thanks to the 3D printing capabilities. As for architecture, they can be applied not only as an element of ornamentation, but also as a functional component of the project, especially concerning climate responsive facades.   
Due to the simplicity of the geometry of C-II-n, such 3D structures are feasible and easy to perform in terms of production and assembly. They are achievable not only with 3D printing, but can also be manually assembled or folded like origami, which allows the use of a much wider range of materials.",
publisher = "Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija",
journal = "Smart Art Knjiga apstrakata / Book of abstracts",
title = "3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments",
pages = "88-87",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1981"
}

Obradović, M.,& Mišić, S.. (2019). 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments. in Smart Art Knjiga apstrakata / Book of abstracts
Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija., 87-88.
https://hdl.handle.net/21.15107/rcub_grafar_1981

Obradović M, Mišić S. 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments. in Smart Art Knjiga apstrakata / Book of abstracts. 2019;:87-88.
https://hdl.handle.net/21.15107/rcub_grafar_1981 .

Obradović, Marija, Mišić, Slobodan, "3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments" in Smart Art Knjiga apstrakata / Book of abstracts (2019):87-88,
https://hdl.handle.net/21.15107/rcub_grafar_1981 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1982
AB  - We have shown that there is a link between the geometry of the CA II-nM’s  with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given  CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s  with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.
PB  - Porto: Aproged - Associação dos Professores de Geometria e de Desenho
C3  - GEOMETRIAS’19: BOOK OF ABSTRACTS
T1  - Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort
SP  - 85
VL  - 89
DO  - 10.24840/978-989-98926-8-2
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2019",
abstract = "We have shown that there is a link between the geometry of the CA II-nM’s  with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given  CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s  with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.",
publisher = "Porto: Aproged - Associação dos Professores de Geometria e de Desenho",
journal = "GEOMETRIAS’19: BOOK OF ABSTRACTS",
title = "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort",
pages = "85",
volume = "89",
doi = "10.24840/978-989-98926-8-2"
}

Obradović, M.,& Mišić, S.. (2019). Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS
Porto: Aproged - Associação dos Professores de Geometria e de Desenho., 89, 85.
https://doi.org/10.24840/978-989-98926-8-2

Obradović M, Mišić S. Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS. 2019;89:85.
doi:10.24840/978-989-98926-8-2 .

Obradović, Marija, Mišić, Slobodan, "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort" in GEOMETRIAS’19: BOOK OF ABSTRACTS, 89 (2019):85,
https://doi.org/10.24840/978-989-98926-8-2 . .

TY  - JOUR
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/999
AB  - As architectural structures, concave cupolae of the second sort (CC II) are suitable for prefabrication, thanks to the uniformity of their elementsregular polygons. This paper discusses ways to subdivide the lateral polyhedral triangle (LPT) of CC II into new regular polygons, triangles and hexagons, which can then tile the whole deltahedral lateral surface, forming patterns applicable in architectural design. The number of different arrangements of triangles and hexagons depends on the number of unit hexagonal cells (tiles) that can be placed within the triangular grid of the equilateral triangle. Considering solutions that involve fragments of k-uniform Euclidean tilings, we explored the ones that arise when the edges of the LPT are subdivided into 3b9 (bN) segments. Without attempting to analyse all the possible cases, we focused on the ones with the D-3 symmetry, in order to propose the simplest solutions for the assembly, so it will not matter if the face of the CC II is rotated or flipped. This results in 30 different solutions, excluding the ones consisting of triangles alone. The solutions found are applicable to all the representatives of CC II. We chose several examples of these results for an architectural design proposal.
PB  - Birkhauser Verlag AG
T2  - Nexus Network Journal
T1  - Tiling the Lateral Surface of the Concave Cupolae of the Second Sort
EP  - 77
IS  - 1
SP  - 59
VL  - 21
DO  - 10.1007/s00004-018-0417-5
ER  - 

@article{
author = "Obradović, Marija",
year = "2019",
abstract = "As architectural structures, concave cupolae of the second sort (CC II) are suitable for prefabrication, thanks to the uniformity of their elementsregular polygons. This paper discusses ways to subdivide the lateral polyhedral triangle (LPT) of CC II into new regular polygons, triangles and hexagons, which can then tile the whole deltahedral lateral surface, forming patterns applicable in architectural design. The number of different arrangements of triangles and hexagons depends on the number of unit hexagonal cells (tiles) that can be placed within the triangular grid of the equilateral triangle. Considering solutions that involve fragments of k-uniform Euclidean tilings, we explored the ones that arise when the edges of the LPT are subdivided into 3b9 (bN) segments. Without attempting to analyse all the possible cases, we focused on the ones with the D-3 symmetry, in order to propose the simplest solutions for the assembly, so it will not matter if the face of the CC II is rotated or flipped. This results in 30 different solutions, excluding the ones consisting of triangles alone. The solutions found are applicable to all the representatives of CC II. We chose several examples of these results for an architectural design proposal.",
publisher = "Birkhauser Verlag AG",
journal = "Nexus Network Journal",
title = "Tiling the Lateral Surface of the Concave Cupolae of the Second Sort",
pages = "77-59",
number = "1",
volume = "21",
doi = "10.1007/s00004-018-0417-5"
}

Obradović, M.. (2019). Tiling the Lateral Surface of the Concave Cupolae of the Second Sort. in Nexus Network Journal
Birkhauser Verlag AG., 21(1), 59-77.
https://doi.org/10.1007/s00004-018-0417-5

Obradović M. Tiling the Lateral Surface of the Concave Cupolae of the Second Sort. in Nexus Network Journal. 2019;21(1):59-77.
doi:10.1007/s00004-018-0417-5 .

Obradović, Marija, "Tiling the Lateral Surface of the Concave Cupolae of the Second Sort" in Nexus Network Journal, 21, no. 1 (2019):59-77,
https://doi.org/10.1007/s00004-018-0417-5 . .

TY  - CONF
AU  - Obradović, Marija
AU  - Grujić, Tatjana
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1943
AB  - In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies
which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves.
PB  - Novi Sad:Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Conference Proceedings „MONGEOMETRIJA 2018"
T1  - Geometry behind the position of stairs: balance in the mind
EP  - 168
SP  - 156
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1943
ER  - 

@conference{
author = "Obradović, Marija and Grujić, Tatjana",
year = "2018",
abstract = "In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies
which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves.",
publisher = "Novi Sad:Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Conference Proceedings „MONGEOMETRIJA 2018"",
title = "Geometry behind the position of stairs: balance in the mind",
pages = "168-156",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1943"
}

Obradović, M.,& Grujić, T.. (2018). Geometry behind the position of stairs: balance in the mind. in Conference Proceedings „MONGEOMETRIJA 2018"
Novi Sad:Faculty of Technical Sciences, University of Novi Sad., 156-168.
https://hdl.handle.net/21.15107/rcub_grafar_1943

Obradović M, Grujić T. Geometry behind the position of stairs: balance in the mind. in Conference Proceedings „MONGEOMETRIJA 2018". 2018;:156-168.
https://hdl.handle.net/21.15107/rcub_grafar_1943 .

Obradović, Marija, Grujić, Tatjana, "Geometry behind the position of stairs: balance in the mind" in Conference Proceedings „MONGEOMETRIJA 2018" (2018):156-168,
https://hdl.handle.net/21.15107/rcub_grafar_1943 .

TY  - GEN
AU  - Marković, Srđan
AU  - Obradović, Marija
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1979
AB  - The idea for this design came from investigation of forms created as “time imprint” of moving 2D and 3D objects through space, while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains “frozen” in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole.
The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the object’s random transformations in 3D space. The transformations are randomly generated and controlled by noise function. 
In order to examine the possibilities of such a creating of spatial forms for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes).
PB  - Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad
PB  - Beograd: Serbian Society for Geometry and Graphics (SUGIG)
T2  - Digital design exhibition “Designing Complexity 2018”
T1  - Spatial forms create by time extrusion of moving objects
SP  - 26
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1979
ER  - 

@misc{
author = "Marković, Srđan and Obradović, Marija",
year = "2018",
abstract = "The idea for this design came from investigation of forms created as “time imprint” of moving 2D and 3D objects through space, while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains “frozen” in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole.
The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the object’s random transformations in 3D space. The transformations are randomly generated and controlled by noise function. 
In order to examine the possibilities of such a creating of spatial forms for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes).",
publisher = "Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad, Beograd: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Digital design exhibition “Designing Complexity 2018”",
title = "Spatial forms create by time extrusion of moving objects",
pages = "26",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1979"
}

Marković, S.,& Obradović, M.. (2018). Spatial forms create by time extrusion of moving objects. in Digital design exhibition “Designing Complexity 2018”
Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad., 26.
https://hdl.handle.net/21.15107/rcub_grafar_1979

Marković S, Obradović M. Spatial forms create by time extrusion of moving objects. in Digital design exhibition “Designing Complexity 2018”. 2018;:26.
https://hdl.handle.net/21.15107/rcub_grafar_1979 .

Marković, Srđan, Obradović, Marija, "Spatial forms create by time extrusion of moving objects" in Digital design exhibition “Designing Complexity 2018” (2018):26,
https://hdl.handle.net/21.15107/rcub_grafar_1979 .

TY  - CONF
AU  - Obradović, Marija
AU  - Marković, Srđan
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1512
AB  - The idea behind this paper is to investigate forms created as time imprint of moving 2D and 3D objects through space while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains frozen in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole. The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the objects random transformations in 3D space. The transformations are randomly generated and controlled by noise function. In order to examine the possibilities of such a creating of 3D shapes for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes). We also explore what kind of "time imprint" in space leaves the chosen starting figure in a free movement, i.e. for a non-geometric path, but also randomly generated one. The given modelling method provides simple and quick, but very intriguing options for creating a wide range of shapes that can be used in various areas of art and design: from graphic design, to a novel way of sculptural and even architectural design. These forms may convincingly represent natural and bionic forms, e.g. hair strands, vegetation growth, etc. The possibility of 3D printing enables the physical materialization of these shapes, suitable for further processing and use for decorative purposes, such as architectural ornaments or jewellery. As an integral part of the research, we include animation which shows the method of generating shapes in the described manner
PB  - Domus Argenia Publisher,
C3  - Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings
T1  - Creating 3D shapes by time extrusion of moving objects
EP  - 238
SP  - 225
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1512
ER  - 

@conference{
author = "Obradović, Marija and Marković, Srđan",
year = "2017",
abstract = "The idea behind this paper is to investigate forms created as time imprint of moving 2D and 3D objects through space while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains frozen in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole. The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the objects random transformations in 3D space. The transformations are randomly generated and controlled by noise function. In order to examine the possibilities of such a creating of 3D shapes for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes). We also explore what kind of "time imprint" in space leaves the chosen starting figure in a free movement, i.e. for a non-geometric path, but also randomly generated one. The given modelling method provides simple and quick, but very intriguing options for creating a wide range of shapes that can be used in various areas of art and design: from graphic design, to a novel way of sculptural and even architectural design. These forms may convincingly represent natural and bionic forms, e.g. hair strands, vegetation growth, etc. The possibility of 3D printing enables the physical materialization of these shapes, suitable for further processing and use for decorative purposes, such as architectural ornaments or jewellery. As an integral part of the research, we include animation which shows the method of generating shapes in the described manner",
publisher = "Domus Argenia Publisher,",
journal = "Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings",
title = "Creating 3D shapes by time extrusion of moving objects",
pages = "238-225",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1512"
}

Obradović, M.,& Marković, S.. (2017). Creating 3D shapes by time extrusion of moving objects. in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings
Domus Argenia Publisher,., 225-238.
https://hdl.handle.net/21.15107/rcub_grafar_1512

Obradović M, Marković S. Creating 3D shapes by time extrusion of moving objects. in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings. 2017;:225-238.
https://hdl.handle.net/21.15107/rcub_grafar_1512 .

Obradović, Marija, Marković, Srđan, "Creating 3D shapes by time extrusion of moving objects" in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings (2017):225-238,
https://hdl.handle.net/21.15107/rcub_grafar_1512 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Stavrić, Milena
AU  - Wiltsche, Albert
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1929
AB  - The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of  the CeP II segments (CP  II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments CP  II-10-A, as well as of CP  II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner.
PB  - Beograd:University of Belgrade, Faculty of Mechanical Engineering
T2  - FME Transactions
T1  - Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron
EP  - 261
IS  - 2
SP  - 256
VL  - 45
DO  - 10.5937/fmet1702256O
ER  - 

@article{
author = "Obradović, Marija and Stavrić, Milena and Wiltsche, Albert",
year = "2017",
abstract = "The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of  the CeP II segments (CP  II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments CP  II-10-A, as well as of CP  II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner.",
publisher = "Beograd:University of Belgrade, Faculty of Mechanical Engineering",
journal = "FME Transactions",
title = "Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron",
pages = "261-256",
number = "2",
volume = "45",
doi = "10.5937/fmet1702256O"
}

Obradović, M., Stavrić, M.,& Wiltsche, A.. (2017). Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron. in FME Transactions
Beograd:University of Belgrade, Faculty of Mechanical Engineering., 45(2), 256-261.
https://doi.org/10.5937/fmet1702256O

Obradović M, Stavrić M, Wiltsche A. Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron. in FME Transactions. 2017;45(2):256-261.
doi:10.5937/fmet1702256O .

Obradović, Marija, Stavrić, Milena, Wiltsche, Albert, "Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron" in FME Transactions, 45, no. 2 (2017):256-261,
https://doi.org/10.5937/fmet1702256O . .

TY  - JOUR
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/875
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - MoNGeometrija 2016
EP  - 204
IS  - 2
SP  - 203
VL  - 45
UR  - https://hdl.handle.net/21.15107/rcub_grafar_875
ER  - 

@article{
author = "Obradović, Marija and Popkonstantinović, Branislav",
year = "2017",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "MoNGeometrija 2016",
pages = "204-203",
number = "2",
volume = "45",
url = "https://hdl.handle.net/21.15107/rcub_grafar_875"
}

Obradović, M.,& Popkonstantinović, B.. (2017). MoNGeometrija 2016. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(2), 203-204.
https://hdl.handle.net/21.15107/rcub_grafar_875

Obradović M, Popkonstantinović B. MoNGeometrija 2016. in FME Transactions. 2017;45(2):203-204.
https://hdl.handle.net/21.15107/rcub_grafar_875 .

Obradović, Marija, Popkonstantinović, Branislav, "MoNGeometrija 2016" in FME Transactions, 45, no. 2 (2017):203-204,
https://hdl.handle.net/21.15107/rcub_grafar_875 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Stavrić, Milena
AU  - Wiltsche, Albert
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/890
AB  - The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of the CeP II segments (C̅P II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments C̅P II-10-A, as well as of C̅P II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner.
AB  - U radu se analizira mogućnost dobijanja složenih poliedarskih oblika kombinovanjem segmenata elongiranih konkavnih piramida druge vrste (CeP II-10, tip A i tip B). U prethodnim istraživanjima, CP II su detaljno obrađeni. Istražuje se dalji potencijal ovih poliedarskih površi, na primeru njihovog spajanja sa Arhimedovim telom, zarubljenim dodekaedrom čije se strane sastoje od dekagona i trouglova. Na dekagonalne strane ovog tela dodajemo podudarne poligone poliedarskih segmenata (C̅P II-10), čime dobijamo nove forme konkavnih kompozitnih poliedara, kao i mogućnost njihovog daljeg preklapanja u poliedarska jedinjenja.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron
T1  - Poliedarske forme nastale spajanjem omotača CP II-10 i zarubljenog dodekaedra
EP  - 261
IS  - 2
SP  - 256
VL  - 45
DO  - 10.5937/fmet1702256O
ER  - 

@article{
author = "Obradović, Marija and Stavrić, Milena and Wiltsche, Albert",
year = "2017",
abstract = "The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of the CeP II segments (C̅P II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments C̅P II-10-A, as well as of C̅P II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner., U radu se analizira mogućnost dobijanja složenih poliedarskih oblika kombinovanjem segmenata elongiranih konkavnih piramida druge vrste (CeP II-10, tip A i tip B). U prethodnim istraživanjima, CP II su detaljno obrađeni. Istražuje se dalji potencijal ovih poliedarskih površi, na primeru njihovog spajanja sa Arhimedovim telom, zarubljenim dodekaedrom čije se strane sastoje od dekagona i trouglova. Na dekagonalne strane ovog tela dodajemo podudarne poligone poliedarskih segmenata (C̅P II-10), čime dobijamo nove forme konkavnih kompozitnih poliedara, kao i mogućnost njihovog daljeg preklapanja u poliedarska jedinjenja.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron, Poliedarske forme nastale spajanjem omotača CP II-10 i zarubljenog dodekaedra",
pages = "261-256",
number = "2",
volume = "45",
doi = "10.5937/fmet1702256O"
}

Obradović, M., Stavrić, M.,& Wiltsche, A.. (2017). Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(2), 256-261.
https://doi.org/10.5937/fmet1702256O

Obradović M, Stavrić M, Wiltsche A. Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron. in FME Transactions. 2017;45(2):256-261.
doi:10.5937/fmet1702256O .

Obradović, Marija, Stavrić, Milena, Wiltsche, Albert, "Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron" in FME Transactions, 45, no. 2 (2017):256-261,
https://doi.org/10.5937/fmet1702256O . .

TY  - CONF
AU  - Obradović, Marija
PY  - 2016
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1464
PB  - Akademska Misao,Beograd, Belgrade
C3  - Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia
T1  - Composite Polyhedral Forms Obtained by Combining Concave Pyramids of the Second Sort with Archimedean Solids
EP  - 131
SP  - 124
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1464
ER  - 

@conference{
author = "Obradović, Marija",
year = "2016",
publisher = "Akademska Misao,Beograd, Belgrade",
journal = "Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia",
title = "Composite Polyhedral Forms Obtained by Combining Concave Pyramids of the Second Sort with Archimedean Solids",
pages = "131-124",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1464"
}

Obradović, M.. (2016). Composite Polyhedral Forms Obtained by Combining Concave Pyramids of the Second Sort with Archimedean Solids. in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia
Akademska Misao,Beograd, Belgrade., 124-131.
https://hdl.handle.net/21.15107/rcub_grafar_1464

Obradović M. Composite Polyhedral Forms Obtained by Combining Concave Pyramids of the Second Sort with Archimedean Solids. in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia. 2016;:124-131.
https://hdl.handle.net/21.15107/rcub_grafar_1464 .

Obradović, Marija, "Composite Polyhedral Forms Obtained by Combining Concave Pyramids of the Second Sort with Archimedean Solids" in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia (2016):124-131,
https://hdl.handle.net/21.15107/rcub_grafar_1464 .