Spatial polyhedra without diagonals

Amos Altshuler; Jürgen Bokowski; Peter Schuchert

doi:10.1007/BF02773687

Spatial polyhedra without diagonals

Amos Altshuler, Jürgen Bokowski, Peter Schuchert

Department of Mathematics

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

6 Scopus citations

Abstract

We provide new polyhedra without diagonals, and we discuss their embeddings in euclidean 3-space with maximal symmetries starting with a complete classification of their combinatorial properties: orientable neighborly 2-pseudomanifolds with 9 vertices or Mendelsohn triple systems S₂(2, 3, 9). This article was motivated by the longstanding and still open question: find a triangulated 2-manifold which can not be embedded in 3-space. Furthermore, we applied tested and improved algorithms for realizing oriented matroids or finding final polynomials.

Original language	English
Pages (from-to)	373-396
Number of pages	24
Journal	Israel Journal of Mathematics
Volume	86
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02773687
State	Published - 1 Oct 1994

ASJC Scopus subject areas

Mathematics (all)

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10.1007/BF02773687

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title = "Spatial polyhedra without diagonals",

abstract = "We provide new polyhedra without diagonals, and we discuss their embeddings in euclidean 3-space with maximal symmetries starting with a complete classification of their combinatorial properties: orientable neighborly 2-pseudomanifolds with 9 vertices or Mendelsohn triple systems S 2(2, 3, 9). This article was motivated by the longstanding and still open question: find a triangulated 2-manifold which can not be embedded in 3-space. Furthermore, we applied tested and improved algorithms for realizing oriented matroids or finding final polynomials.",

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year = "1994",

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T1 - Spatial polyhedra without diagonals

AU - Altshuler, Amos

AU - Bokowski, Jürgen

AU - Schuchert, Peter

PY - 1994/10/1

Y1 - 1994/10/1

N2 - We provide new polyhedra without diagonals, and we discuss their embeddings in euclidean 3-space with maximal symmetries starting with a complete classification of their combinatorial properties: orientable neighborly 2-pseudomanifolds with 9 vertices or Mendelsohn triple systems S 2(2, 3, 9). This article was motivated by the longstanding and still open question: find a triangulated 2-manifold which can not be embedded in 3-space. Furthermore, we applied tested and improved algorithms for realizing oriented matroids or finding final polynomials.

AB - We provide new polyhedra without diagonals, and we discuss their embeddings in euclidean 3-space with maximal symmetries starting with a complete classification of their combinatorial properties: orientable neighborly 2-pseudomanifolds with 9 vertices or Mendelsohn triple systems S 2(2, 3, 9). This article was motivated by the longstanding and still open question: find a triangulated 2-manifold which can not be embedded in 3-space. Furthermore, we applied tested and improved algorithms for realizing oriented matroids or finding final polynomials.

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DO - 10.1007/BF02773687

M3 - Article

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1-3

ER -

Spatial polyhedra without diagonals

Abstract

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