Congpei An

Minkowski Polytopes of Spherical Designs: High-Order Isotropy and Quantitative Sphericity

Let $X_N=\{x_1,\dots,x_N\}\subset \Sph^2$ be a spherical $t$-design of strength $t\ge2$, and let $\mu_X$ be its empirical measure. Minkowski's theorem associates with $X_N$ a convex polytope $P_X\subset\R^3$, unique up to translation, whose facet normals are the design nodes and whose facets all have area $4\pi/N$; equ...