Abstract Regular Polytopes of Finite Irreducible Coxeter Groups

2025/01/02 by Chen, Malcolm Hoong Wai, Rowley, Peter
#20B25 #20F55 #52B11 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2501.01288

Abstract

Here, for W the Coxeter group D_n where n > 4, it is proved that the maximal rank of an abstract regular polytope for W is n - 1 if n is even and n if n is odd. Further it is shown that W has abstract regular polytopes of rank r for all r such that 3 ≤ r ≤ n - 1, if n is even, and 3 ≤ r ≤ n, if n is odd. The possible ranks of abstract regular polytopes for the exceptional finite irreducible Coxeter groups are also determined.

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