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.
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 . .
,