Self-dual Wulff shapes and spherical convex bodies of constant width $\pi /2$

Abstract

For any Wulff shape, its dual Wulff shape is naturally defined. A self-dual Wulff shape is a Wulff shape equaling its dual Wulff shape exactly. In this paper, it is shown that a Wulff shape is self-dual if and only if the spherical convex body induced by it is of constant width $\pi /2$.

arXiv comment9 pages, 5 figures