# Transitivity (InstanceTopic, 3)

### From Hi.gher. Space

**Transitivity** is a property applied to the hypercells of a polytope. A polytope is said to be *n*-transitive iff there is an automorphism on the polytope mapping any particular *n*-cell to any other *n*-cell in the polytope.

Usually, *n*-transitivity for 0 ≤ *n* ≤ 3 is referred to as vertex-, edge-, face- and cell-transitivity respectively. In addition, a polytope exhibiting *n*-transitivity is *isogonal*, *isotoxal*, *isohedral*, *isochoric*, *isoteral*, *isopetal* etc.