A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

Details A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

1993-09-08

arxiv.org/abs/hep-th/9309043v2

J.Math.Phys. 35 (1994) 6076-6095

Physics

High Energy Physics

High Energy Physics - Theory

Plain TeX, 26 pages (eqn. (86) corrected)

Scientific paper

10.1063/1.530729

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.

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