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Ranks of Abstract Regular Polytopes for Finite Irreducible Coxeter Groups

Determines which ranks of abstract regular polytope (equivalently, string C-group) each finite irreducible Coxeter group admits. For the family Dn with n greater than 4 the maximal rank is n-1 when n is even and n when n is odd, with C-strings realized at every intermediate rank down to 3; the maximal ranks are also tabulated for the exceptional groups H3, H4, F4, E6, E7 and E8.

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Abstract Regular Polytopes of Finite Irreducible Coxeter Groups

Determines the possible ranks of abstract regular polytopes admitted by the finite irreducible Coxeter groups. An abstract regular polytope for a group corresponds to a string C-group: a generating s…