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

J. S. Dowker
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Abstract

A derivation of the Cesàro-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 Schläfli reciprocal.

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J. S. Dowker. 1993-09-10. A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope. https://doi.org/10.1063/1.530729

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