Surface (body) of constant width is the surface such that the distance between any two parallel tangent (supporting) planes is constant.

Meissner body is a body of constant width by properly smoothing the edges of a Reuleaux tetrahedron, that is an intersection of four balls placed in the vertexes of a regular tetrahedron and with radii equal to its side-length. Unlike the Reuleaux triangle, the Reuleaux tetrahedron is not a body of constant width. Upon smoothing properly 3 out of 6 edges of this curvlinear polyhedron, one gets Meissner body of contant width.

Meissner body is not rotationally symmetric, but has a discrete symmetry group.