# dim(SimplicialComplex) -- dimension of a simplicial complex

## Synopsis

• Function: dim
• Usage:
dim D
• Inputs:
• Outputs:
• an integer, the maximum number of vertices in a face minus one

## Description

The following simplicial complex consists of a tetrahedron, with two triangles attached, two more edges and an isolated vertex. Since the largest facet has 4 vertices, this complex has dimension 3.
 i1 : R = ZZ[a..h]; i2 : D = simplicialComplex{a*b*c*d, a*b*e, c*d*f, f*g, g*a, h} o2 = | h fg ag cdf abe abcd | o2 : SimplicialComplex i3 : dim D o3 = 3
The void complex has dimension minus infinity, while the irrelevant complex has dimension -1.
 i4 : void = simplicialComplex monomialIdeal 1_R; i5 : dim void o5 = -infinity o5 : InfiniteNumber i6 : irrelevant = simplicialComplex {1_R}; i7 : dim irrelevant o7 = -1