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Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron

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2017
Polyhedral Forms Obtained by Combinig Lateral Sheet of CP II-10 and Truncated Dodecahedron (1.150Mb)
Authors
Obradović, Marija
Stavrić, Milena
Wiltsche, Albert
Contributors
Rašuo, Boško
Stevanović, Vladimir
Sedmak, Simon
Popkonstantinović, Branislav
Article (Published version)
,
Faculty of Mechanical Engineering, Belgrade
Metadata
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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.

Keywords:
concave polyhedra / composite polyhedra / truncated dodecahedron / CP II-10 / augmentation / incavation
Source:
FME Transactions, 2017, 45, 2, 256-261
Publisher:
  • Beograd:University of Belgrade, Faculty of Mechanical Engineering
Funding / projects:
  • Развој нових информационо-комуникационих технологија, коришћењем напредних математичких метода, са применама у медицини, телекомуникацијама, енергетици, заштитити националне баштине и образовању (III44006) - MПНТР
Note:
  • https://www.mas.bg.ac.rs/_media/istrazivanje/fme/vol45/2/contents_fme_vol_45_no_2.pdf [https://www.mas.bg.ac.rs/istrazivanje/fme/start]

DOI: 10.5937/fmet1702256O

ISSN: 1451-2092

WoS: 000408082400010

Scopus: 2-s2.0-85016239203
[ Google Scholar ]
1
1
URI
https://grafar.grf.bg.ac.rs/handle/123456789/1929
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за математику, физику и нацртну геометрију
Institution/Community
GraFar
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 . .

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