Curve of Constant Width - Generalizations

Generalizations

Δ curves, which can be rotated in the equilateral triangle, have many similar properties to curves of constant width.

The generalization of the definition of bodies of constant width to convex bodies in R³ and their boundaries leads to the concept of surface of constant width (in the case of a Reuleaux triangle, this does not lead to a Reuleaux tetrahedron, but to Meissner bodies). There is also the concept of space curves of constant width, whose widths are defined by tangent planes.