Simplicial cross-polytopic d-arrangements
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.
scientific article; zbMATH DE number 4054465
scientific article