Polynomial Invariants and Harmonic Functions Related to Exceptional Regular Polytopes
Polynomial Invariants and Harmonic Functions Related to Exceptional Regular Polytopes
Abstract We compute certain polynomial invariants for the finite reflection groups of the types 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 …