Developable roller

These bodies are cut in two at their symmetry plane and the two halves are reunited after being rotated at an offset angle relative to each other.

Like the prime polysphericons the polycons are based on regular polygons but consist of identical pieces of only one type of cone with no frustum parts.

In the case of the polycons and Platonicons, as well as some of the prime polysphericons, the path of their center of mass consists of circular arcs.

In the case of the prime polysphericons that have surfaces that contain cylindrical parts the path is a combination of circular arcs and straight lines.

A general expression for the shape of the path of the TDR convex hulls center of mass has yet to be derived.

All prime polysphericons, polycons, and platonicons and some of the TDR convex hulls share this property.

In order for a TDR convex hull to maintain constant height the following must hold: Where a and b are the half minor and major axes of the elliptic arcs, respectively, and c is the distance between their centers.