A convex surface which has in every direction the same diameter
is called “surface of constant width”. The diameter in any given
direction is the distance between the two (opposite) tangent
planes orthogonal to that direction.

Surfaces of constant width can move around in a cubical box which they
touch at all six faces. This “rotation” is more a wobbling around since
no “midpoint” stays fixed.

Explicit Formulas

A convex surface, given as the image of a map F: S^2 ⟶ R^3, can be defined
by its "support function" h : S^2 ⟶ R+ by putting for each vector n in S^2

F(n) = h(n) * n + grad h(n)

(grad h understood as tangent vector of S^2)

The vector n is the exterior normal of the surface at the point F(n).

The image of F is a surface of constant width w, iff h(n) + h(-n) = w.