Volume Computation and Comparison for Four-Dimensional Bodies of Constant Width
We compute and compare the volumes of explicit four-dimensional bodies of constant width one. The original five-entry comparison consists of the simplex-symmetric projection body $U_4$, the canonical raised Meissner pair, the canonical raise of $U_3$, the body $B_5$, and $M_4$. We combine exact geometric formulas, numerical integration, interval enclosures and inscribed rational polytopes to obtain a certified strict ordering of their volumes. We also compare $U_4$ with the direct four-dimensional AMO peabody. The two raised Meissner bodies are proved noncongruent but exactly equal in…
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