Simplicial cross-polytopic d-arrangements
type: Item
instance of: scholarly article
title: Simplicial cross-polytopic d-arrangements
zbMATH Open document ID: 0646.52005
DOI: 10.1007/BF00181614
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: Following an observation of B. Grünbaum, the projective d-arrangement of facet hyperplanes of a regular polytope completed by some of its mirror symmetry hyperplanes and the hyperplanes at infinity can be simplicial, i.e. can have only simplex cells. In the case of a cross- polytope, earlier papers of B. Grünbaum, G. C. Shephard and the authors contain eleven types of such arrangements, more precisely four 2- arrangements, six 3-arrangements and one 4-arrangement. In the present paper it is shown that (besides three additional, trivial 1-arrangements) no further projective d-arrangement (d\(\geq 1)\), corresponding with a cross-polytope in the described manner, is simplicial.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4054465
zbMATH Keywords: projective arrangements of hyperplanes
zbMATH Keywords: simplicial arrangement
zbMATH Keywords: mirror symmetry
zbMATH Keywords: cross-polytope
author: Gerald L. Alexanderson
author: John E. Wetzel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181614
OpenAlex ID: W2053183717
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description: scientific article; zbMATH DE number 4054465