Self-dual Wulff shapes and spherical convex bodies of constant width $π/{2}$

preprint2016arXivOpen access

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 $π/{2}$ .

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Self-dual Wulff shapes and spherical convex bodies of constant width $π/{2}$

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Self-dual Wulff shapes and spherical convex bodies of constant width π/2π/{2}π/2

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Self-dual Wulff shapes and spherical convex bodies of constant width $π/{2}$