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Simplicial arrangements associated with the 24-cell

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Abstract

Let ℓ = A 14 (49) be the 4-arrangement in real projective 4-space that includes all 24 facet hyperplanes of the 24-cellT, its 24 hyperplanes of mirror symmetry, and the hyperplane at infinity. In this paper we show that ℝ is theonly simplicial 4-arrangement formed by including some of the hyperplanes of mirror symmetry and possibly the hyperplane at infinity with the 24 facet hyperplanes ofT. Only one other simplicial 4-arrangement is known that does not lie in a natural sequence of arrangements that are simplicial in each dimension. Two of the simplicial 3-arrangements induced by X were not previously in the literature, so 19 joinirreducible simplicial 3-arrangements are currently known.

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  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, 61801, Urbana, IL, USA

    John E. Wetzel

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  1. John E. Wetzel
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Wetzel, J.E. Simplicial arrangements associated with the 24-cell. J Geom 45, 177–200 (1992). https://doi.org/10.1007/BF01225776

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