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The concept of rigid spherical t-designs was introduced by Eiichi Bannai. We want to find examples of rigid but not tight spherical designs. Sali investigated the case when X is an orbit of a finite r...eflection group and proved that X is rigid if and only if tight for the groups A_n, B_n, C_n, D_n, E_6, E_7, F_4, H_3. There are two cases left open, namely the group E_8 and the isometry group H_4 of the four-dimensional regular polytope, the 600-cell. In this paper, we study the rigidity of spherical t-designs X that are orbits of a finite reflection groups E_8 and H_4, and prove that X is rigid if and only if tight or the 600-cell.続きを見る
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