# boundary(SimplicialComplex) -- the boundary simplicial complex of D

## Synopsis

• Function: boundary
• Usage:
boundary D
• Inputs:
• Outputs:
• , the boundary simplicial complex, i.e. the subcomplex of D consisting of all nonmaximal faces of D

## Description

The boundary of the standard 3-simplex is the 2-sphere.
 i1 : R = ZZ[a..d]; i2 : simplex = simplicialComplex{a*b*c*d} o2 = | abcd | o2 : SimplicialComplex i3 : sphere = boundary simplex o3 = | bcd acd abd abc | o3 : SimplicialComplex i4 : fVector sphere o4 = HashTable{-1 => 1} 0 => 4 1 => 6 2 => 4 o4 : HashTable i5 : fVector simplex o5 = HashTable{-1 => 1} 0 => 4 1 => 6 2 => 4 3 => 1 o5 : HashTable
Facets may be of different dimensions.
 i6 : R = ZZ[a..g]; i7 : D = simplicialComplex{a*b*c,a*d,d*f,g*c,e,f*g} o7 = | fg cg df e ad abc | o7 : SimplicialComplex i8 : E = boundary D o8 = | g f d bc ac ab | o8 : SimplicialComplex i9 : fVector D o9 = HashTable{-1 => 1} 0 => 7 1 => 7 2 => 1 o9 : HashTable i10 : fVector E o10 = HashTable{-1 => 1} 0 => 6 1 => 3 o10 : HashTable