| Title: | Classification of convex polyhedra by their rotational orbit Euler characteristic |
|---|
| Authors: | ID Kovič, Jurij (Author) |
|---|
| Files: |  RAZ_Kovic_Jurij_i2017.pdf (272,96 KB)
MD5: 34C55610C9518FB2AA931FEDFA9E96B9
|
|---|
| Language: | English |
|---|
| Work type: | Unknown |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | Let ▫$\mathcal P$▫ be a polyhedron whose boundary consists of flat polygonal faces on some compact surface ▫$S(\mathcal P)$▫ (not necessarily homeomorphic to the sphere ▫$S^{2}$)▫. Let ▫$vo_{R}(\mathcal P), eo_{R}(\mathcal P)$▫, ▫$ fo_{R}(\mathcal P)$▫ be the numbers of rotational orbits of vertices, edges and faces, respectively, determined by the group ▫$G = G_{R}(P)$▫ of all the rotations of the Euclidean space ▫$E^{3}$▫ preserving ▫$\mathcal P$▫. We define the ''rotational orbit Euler characteristic'' of ▫$\mathcal P$▫ as the number ▫$Eo_{R}(\mathcal P) = vo_{R}(\mathcal P) - eo_{R}(\mathcal P) + fo_{R}(\mathcal P)$▫. Using the Burnside lemma we obtain the lower and the upper bound for ▫$Eo_{R}(\mathcal P)$▫ in terms of the genus of the surface ▫$S(P)$▫. We prove that ▫$Eo_{R} \in \lbrace 2,1,0,-1\rbrace $▫ for any convex polyhedron ▫$\mathcal P$▫. In the non-convex case ▫$Eo_{R}$▫ may be arbitrarily large or small. |
|---|
| Keywords: | polyhedron, rotational orbit, Euler characteristic |
|---|
| Year of publishing: | 2017 |
|---|
| Number of pages: | str. 23-30 |
|---|
| Numbering: | Vol. 13, no. 1 |
|---|
| PID: | 20.500.12556/RUP-17627  |
|---|
| UDC: | 514.113.5:519.1 |
|---|
| ISSN on article: | 1855-3966 |
|---|
| COBISS.SI-ID: | 17897561 |
|---|
| Publication date in RUP: | 03.01.2022 |
|---|
| Views: | 2050 |
|---|
| Downloads: | 19 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
