A simplicial 4-arrangement of 33 hyperplanes
type: Item
instance of: scholarly article
title: A simplicial 4-arrangement of 33 hyperplanes
zbMATH Open document ID: 0628.52007
DOI: 10.1007/BF00181597
published in: Geometriae Dedicata
publication date: 1987-01-01T00:00:00Z
review text: We show that the projective d-arrangement \({\mathfrak C}^ d\) formed by the facet hyperplanes of a cross-polytope, its hyperplanes of mirror symmetry, and the hyperplane at infinity is simplicial precisely for \(d\leq 4.\) The arrangement \({\mathfrak C}^ 4\) is the only simplicial 4-arrangement presently known that does not lie in a natural sequence of analogous arrangements that are simplicial in each dimension. It has flat vector \({\mathfrak g}=<409,746\), \(290,33>\) and face vector \({\mathfrak f}=<409,4104,12336,14400,5760>\).
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 4022035
zbMATH Keywords: simplicial projective d-arrangements of hyperplanes
author: Gerald L. Alexanderson
author: John E. Wetzel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181597
OpenAlex ID: W2087540732
description: scientific article; zbMATH DE number 4022035