The weakly neighborly polyhedral maps on the torus

Ulrich Brehm, Amos Altshuler

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)227-238
Number of pages12
JournalGeometriae Dedicata
Volume18
Issue number3
DOIs
StatePublished - 1 Aug 1985

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