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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]

Bibliography[edit | edit source]

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