Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].
A recursive construction of projective cubature formulas and related isometric embeddings
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
A recursive construction is presented for the projective cubature formulas of index $p$ on the unit spheres $S(m,K)\subset K^m$ where $K$ is $R$ or $C$, or $H$. This yields a lot of new upper bounds for the minimal number of nodes $n=N_K(m,p)$ in such formulas or, equivalently, for the minimal $n$ such that there exists an isometric embedding $\ell_{2; K}^m \rightarrow \ell_{p; K}^n$.
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Optimal measures for p-frame energies on spheres
Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].