# fc -- The faces of a complex.

• Usage:
fc(C)
fc(C,d)
• Inputs:
• Outputs:

## Description

Returns a list with entries lists with the faces of C starting in dimension -1. If d is given then faces of dimension d are returned.

 i1 : R=QQ[x_0..x_5] o1 = R o1 : PolynomialRing i2 : C=boundaryCyclicPolytope(3,R) o2 = 2: x x x x x x x x x x x x x x x x x x x x x x x x 0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5 o2 : complex of dim 2 embedded in dim 5 (printing facets) equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1 i3 : fc C o3 = {{{}}, {x , x , x , x , x , x }, {x x , x x , x x , x x , x x , x x , 0 1 2 3 4 5 0 1 0 2 1 2 0 3 2 3 0 4 ------------------------------------------------------------------------ x x , x x , x x , x x , x x , x x }, {x x x , x x x , x x x , x x x , 3 4 0 5 1 5 2 5 3 5 4 5 0 1 2 0 2 3 0 3 4 0 1 5 ------------------------------------------------------------------------ x x x , x x x , x x x , x x x }, {}, {}, {}} 1 2 5 2 3 5 0 4 5 3 4 5 o3 : List i4 : fc(C,1) o4 = {x x , x x , x x , x x , x x , x x , x x , x x , x x , x x , x x , x x } 0 1 0 2 1 2 0 3 2 3 0 4 3 4 0 5 1 5 2 5 3 5 4 5 o4 : List

## Ways to use fc :

• "fc(Complex)"
• "fc(Complex,ZZ)"

## For the programmer

The object fc is .