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2002 Polynomial invariants and harmonic functions related to exceptional regular polytopes
Katsunori Iwasaki, Atsufumi Kenma, Keiji Matsumoto
Experiment. Math. 11(2): 313-319 (2002).

Abstract

We compute certain polynomial invariants for the finite reflection groups of the types {\small $H_3$, $H_4$ and $F_4$}. Using this result, we explicitly determine the solution space of functions satisfying a mean value property related to the exceptional regular polytopes, namely, the icosahedron and dodecahedron in three dimensions and the 24-cell, 600-cell, and 120-cell in four dimensions.

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Katsunori Iwasaki. Atsufumi Kenma. Keiji Matsumoto. "Polynomial invariants and harmonic functions related to exceptional regular polytopes." Experiment. Math. 11 (2) 313 - 319, 2002.

Information

Published: 2002
First available in Project Euclid: 3 September 2003

zbMATH: 1116.52300
MathSciNet: MR1959272

Subjects:
Primary: 52B11
Secondary: 20F55

Keywords: exceptional regular polytopes , finite reflection groups , Harmonic functions , mean value property , Polynomial invariants

Rights: Copyright © 2002 A K Peters, Ltd.

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Vol.11 • No. 2 • 2002
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