pure simplicial complex

A finite simplicial complex is pure if each facet has the same dimension.

For example, any polytope is pure, but the simplicial complex

$$\{\mathrm{\varnothing },a,b,c,d,ab,ac,bc,cd,abc\}$$

is not pure because $cd$ and $abc$ are facets with different dimensions.

Title	pure simplicial complex
Canonical name	PureSimplicialComplex
Date of creation	2013-03-22 14:18:52
Last modified on	2013-03-22 14:18:52
Owner	mps (409)
Last modified by	mps (409)
Numerical id	5
Author	mps (409)
Entry type	Definition
Classification	msc 55U10
Classification	msc 52B99