# star -- star of a face in a simplicial complex

## Synopsis

• Usage:
star(D,f)
• Inputs:
• f, , a monomial representing a face of the simplicial complex D
• Outputs:
• , the star of f in D

## Description

The star of a face $f$ in $D$ is the simplicial complex whose faces are the subsets $g$ with $f \cup g$ is a face of $D$.

The bow-tie complex.

 i1 : R = QQ[x_1..x_5]; i2 : bowtie = simplicialComplex {x_1*x_2*x_3,x_3*x_4*x_5} o2 = | x_3x_4x_5 x_1x_2x_3 | o2 : SimplicialComplex i3 : star(bowtie,x_3) o3 = | x_3x_4x_5 x_1x_2x_3 | o3 : SimplicialComplex i4 : star(bowtie,x_1*x_2) o4 = | x_1x_2x_3 | o4 : SimplicialComplex

The 3-simplex and a copy of its boundary glued along a triangle.

 i5 : R = QQ[a..e]; i6 : D = simplicialComplex {a*b*c*d, b*c*e, b*d*e, c*d*e} o6 = | cde bde bce abcd | o6 : SimplicialComplex i7 : star(D,b*c*d) o7 = | abcd | o7 : SimplicialComplex i8 : star(D,b) o8 = | bde bce abcd | o8 : SimplicialComplex