# isFace -- tests if the first argument is a face of the second

## Synopsis

• Usage:
b = isFace(X,Y)
• Inputs:
• X, , or Polyhedron
• Y, an element of the same class as X
• Outputs:
• b, , true if X is a face of Y, false otherwise

## Description

Both arguments must lie in the same ambient space. Then isFace computes all faces of Y with the dimension of X and checks if one of them is X.

 i1 : P = hypercube 3 o1 = P o1 : Polyhedron i2 : Q = convexHull matrix{{1,1,1},{1,1,-1},{1,-1,1}} o2 = Q o2 : Polyhedron i3 : isFace(Q,P) o3 = false

Thus, Q is not a face of P, but we can extend it to a face.

 i4 : v = matrix{{1},{-1},{-1}}; 3 1 o4 : Matrix ZZ <--- ZZ i5 : Q = convexHull{Q,v} o5 = Q o5 : Polyhedron i6 : isFace(Q,P) o6 = true

## Ways to use isFace :

• "isFace(Cone,Cone)"
• "isFace(Polyhedron,Polyhedron)"

## For the programmer

The object isFace is .