On realizing symmetric 3-polytopes

Joseph Zaks

doi:10.1007/BF02771576

On realizing symmetric 3-polytopes

Joseph Zaks

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the analogue of Eberhard's Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.

Original language	English
Pages (from-to)	244-251
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF02771576
State	Published - Jun 1971
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF02771576

Cite this

@article{66b936bcceb24b339a279b32fc530d8e,

title = "On realizing symmetric 3-polytopes",

abstract = "We prove the analogue of Eberhard's Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.",

author = "Joseph Zaks",

year = "1971",

month = jun,

doi = "10.1007/BF02771576",

language = "English",

volume = "10",

pages = "244--251",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - On realizing symmetric 3-polytopes

AU - Zaks, Joseph

PY - 1971/6

Y1 - 1971/6

N2 - We prove the analogue of Eberhard's Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.

AB - We prove the analogue of Eberhard's Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.

UR - https://www.scopus.com/pages/publications/51649184899

U2 - 10.1007/BF02771576

DO - 10.1007/BF02771576

M3 - Article

AN - SCOPUS:51649184899

SN - 0021-2172

VL - 10

SP - 244

EP - 251

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

On realizing symmetric 3-polytopes

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this