Quasi-convexity

Quasi-convexity is a property of polyhedra related to convexity. It is primarily examined with respects to Stewart toroids, however there are spherical polyhedra which are quasi-convex but not convex (e.g. excavated icosahedron).

Definition
A polyhedron, $P$, is quasi-convex if all of the edges of its convex hull are also edges of $P$.

History
The concept of quasi-convexity was originally suggested by Norman Johnson as a restriction on regular faced toroidal polyhedra to a finite set. The property first appears as the property "(Q)" in Adventures Amoung the Toroids, written by Bonnie Stewart.