GraFar - Repository of the Faculty of Civil Engineering
Faculty of Civil Engineering of the University of Belgrade
    • English
    • Српски
    • Српски (Serbia)
  • English 
    • English
    • Serbian (Cyrillic)
    • Serbian (Latin)
  • Login
View Item 
  •   GraFar
  • GraFar
  • Катедра за математику, физику и нацртну геометрију
  • View Item
  •   GraFar
  • GraFar
  • Катедра за математику, физику и нацртну геометрију
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Three-Dimensional Rosettes Based on the Geometry of Concave Deltahedral Surfaces

Thumbnail
2020
THREE-DIMENSIONAL ROSETTES BASED ON THE GEOMETRY OF CONCAVE DELTAHEDRAL SURFACES (6.286Mb)
Authors
Mišić, Slobodan
Obradović, Marija
Milakić, Mirjana
Contributors
Prosen, Milan
Conference object (Published version)
,
Faculty of Applied Arts, Belgrade
Metadata
Show full item record
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 obtain...ed 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.

Keywords:
rosette / polyhedron / architecture / triangle / geometry
Source:
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
Publisher:
  • Факултет примењених уметности, Београд, 2020 Faculty of Applied Arts, Belgrade, 2020
Funding / projects:
  • Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 200092 (University of Belgrade, Faculty of Civil Engineering) (RS-200092)
Note:
  • https://2019.smartart-conference.rs/wp-content/uploads/2020/11/ZbornikSmartArt2019.pdf

ISBN: 978-86-80245-40-9

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_grafar_2202
URI
https://grafar.grf.bg.ac.rs/handle/123456789/2202
Collections
  • Катедра за математику, физику и нацртну геометрију
  • Radovi istraživača / Researcher's publications
Institution/Community
GraFar
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 .

DSpace software copyright © 2002-2015  DuraSpace
About the GraFar Repository | Send Feedback

OpenAIRERCUB
 

 

All of DSpaceCommunitiesAuthorsTitlesSubjectsThis institutionAuthorsTitlesSubjects

Statistics

View Usage Statistics

DSpace software copyright © 2002-2015  DuraSpace
About the GraFar Repository | Send Feedback

OpenAIRERCUB