# Quasi-convexity

Jump to navigation
Jump to search

**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[edit | edit source]

A polyhedron, P, is quasi-convex if all of the edges of its convex hull are also edges of P.^{[1]}

## History[edit | edit source]

The concept of quasi-convexity was originally suggested by Norman Johnson as a restriction on regular faced toroidal polyhedra to a finite set.^{[2]} The property first appears as the property "(Q)" in *Adventures Amoung the Toroids*, written by Bonnie Stewart.

## References[edit | edit source]

- ↑ Stewart (1964:77)
- ↑ Stewart (1964:3)

## Bibliography[edit | edit source]

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