The weakly neighborly polyhedral maps on the torus

Ulrich Brehm; Amos Altshuler

doi:10.1007/BF00181222

The weakly neighborly polyhedral maps on the torus

Ulrich Brehm, Amos Altshuler

Department of Mathematics

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

7 Scopus citations

Abstract

A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without a boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just five distinct w.n.p. maps on the torus, and that only three of them are geometrically realizable as polyhedra with convex faces.

Original language	English
Pages (from-to)	227-238
Number of pages	12
Journal	Geometriae Dedicata
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/BF00181222
State	Published - 1 Aug 1985

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF00181222

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title = "The weakly neighborly polyhedral maps on the torus",

abstract = "A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without a boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just five distinct w.n.p. maps on the torus, and that only three of them are geometrically realizable as polyhedra with convex faces.",

author = "Ulrich Brehm and Amos Altshuler",

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N2 - A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without a boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just five distinct w.n.p. maps on the torus, and that only three of them are geometrically realizable as polyhedra with convex faces.

AB - A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without a boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just five distinct w.n.p. maps on the torus, and that only three of them are geometrically realizable as polyhedra with convex faces.

UR - https://www.scopus.com/pages/publications/34250116214

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DO - 10.1007/BF00181222

M3 - Article

AN - SCOPUS:34250116214

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 3

ER -

The weakly neighborly polyhedral maps on the torus

Abstract

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