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A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope (1994)

Dowker, J. S.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 35 (1994), S. 6076-6095

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: 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-smooth boundaries. Several results are obtained that relate the coefficients, bi, in the Shephard–Todd polynomial to the geometry of the fundamental domain. For the 3-sphere, it is shown that b4 is given by the ratio of the volume of the fundamental tetrahedron to its Schläfli reciprocal.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530729

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