# face -- Generate a face.

## Synopsis

• Usage:
face(L)
face(S)
face(L,C)
face(L,C,d,j)
• Inputs:
• Outputs:

## Description

Generate a Face F from a list L (or set S) of vertices. If the additional argument C is given it sets F.ofComplex={C} to store the complex of which F is a face of.

If d and j are given then F.indices={{d,j}} for storing the face dimension d and its index j in (F.ofComplex)#0.

 i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing i2 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0) o2 = ideal (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o2 : Ideal of R i3 : C=idealToComplex I o3 = 1: x x x x x x x x x x 0 2 0 3 1 3 1 4 2 4 o3 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1 i4 : F=C.fc_1_0 o4 = x x 0 2 o4 : face with 2 vertices i5 : F==face(vert F,C,1,0) o5 = true

• Face -- The class of all faces of complexes or co-complexes.
• Complex -- The class of all embedded complexes.
• CoComplex -- The class of all embedded co-complexes.

## Ways to use face :

• "face(List)"
• "face(List,Complex)"
• "face(List,Complex,ZZ,ZZ)"
• "face(Set)"

## For the programmer

The object face is .