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A simplicial 4-arrangement of 33 hyperplanes

โœ Scribed by G. L. Alexanderson; John E. Wetzel

Publisher
Springer
Year
1987
Tongue
English
Weight
394 KB
Volume
24
Category
Article
ISSN
0046-5755

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โœฆ Synopsis

We show in this paper that the projective d-arrangement I$ a formed by the facet hyperplanes of a cross-polytope, its hyperplanes of mirror symmetry, and the hyperplane at infinity is simplicial precisely for d ~< 4.

The arrangement 1$ 4 is the only simplicial d-arrangement presently known that does not lie in a natural sequence of analogous arrangements that are simplicial in each dimension. It has flat vector g = (409, 746, 290, 33) and face vector f = (409, 4104, 12336, 14400, 5760).

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