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Solid of Constant Width

A solid of constant width is an analog of a curve of constant width to three dimensions. Specifically, it is a convex body having the property that any two parallel supporting planes which contain the body between them are at a fixed distance apart (Bogosel 2023).

Solids of constant width include the Meissner tetrahedra and more generally the Meissner polyhedra.

See also

Curve of Constant Width, Meissner Polyhedron, Meissner Tetrahedra, Supporting Hyperplane

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References

Bayen, T.; Lachand-Robert, T.; and Oudet, É. "Analytic Parametrization of Three-Dimensional Bodies of Constant Width." Arch. Ration. Mech. Anal. 186, 225-249, 2007.Bogosel, B. "Volume Computation for Meissner Polyhedra and Applications." 25 Oct 2023. https://arxiv.org/abs/2310.17672.Croft, H. T.; Falconer, K. J.; and Guy, R. K. "Minimal Bodies of Constant Width." §A22 in Unsolved Problems in Geometry. New York: Springer-Verlag, p. 34, 1991.Lachand-Robert, T. and Oudet, É. "Bodies of Constant Width in Arbitrary Dimension." Math. Nachr. 280, 740-750, 2007.

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Solid of Constant Width

Cite this as:

Weisstein, Eric W. "Solid of Constant Width." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SolidofConstantWidth.html

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