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Geometric Properties of the “Flower” Concave Antiprisms of the Second Sort

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2020
GEOMETRIC PROPERTIES OF THE “FLOWER” CONCAVE ANTIPRISMS OF THE SECOND SORT (4.109Mb)
Authors
Obradović, Marija
Contributors
Jeli, Zorana
Conference object (Published version)
,
Serbian Society for Geometry and Graphics (SUGIG)
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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.
Keywords:
concave polyhedron / concave polygon / polygon elevation / antiprism / isotoxal / constructive geometry
Source:
PROCEEDINGS of The 7th International Scientific Conference on Geometry and Graphics moNGeomatrija2020, 2020, 13-26
Publisher:
  • Belgrade: Serbian Society for Geometry and Graphics (SUGIG); Faculty of Mechanical Engineering, University of Belgrade
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:
  • http://mongeometrija.com/attachments/article/417/Plan_i_program.pdf Predavanje po pozivu / Invited lecturer

ISBN: 978-86-6060-046-4

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_grafar_2206
URI
https://grafar.grf.bg.ac.rs/handle/123456789/2206
Collections
  • Катедра за математику, физику и нацртну геометрију
Institution/Community
GraFar
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 .

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