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.

Bibliography

• Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.