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# 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 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 8 o1 : Polyhedron i2 : Q = convexHull matrix{{1,1,1},{1,1,-1},{1,-1,1}} o2 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 3 number of rays => 0 number of vertices => 3 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 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 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 .