cayley -- constructs the Cayley sum of polytopes

• Usage:

  cayley(P1,P2),

  cayley(P1,P2,k),

  cayley(P1,P2,P3),

  cayley(P1,P2,P3,k),

  cayley(L),

  cayley(L,k),

  cayley(M1,M2),

  cayley(M1,M2,k),

  cayley(M1,M2,M3),

  cayley(M1,M2,M3,k)

• Inputs:
  • P1, a convex polyhedron,
  • P2, a convex polyhedron,
  • P3, a convex polyhedron,
  • M1, a matrix,
  • M2, a matrix,
  • M3, a matrix,
  • k, an integer,
  • L, a list,
• Outputs:
  • a convex polyhedron,

i1 : P=convexHull(matrix{{0,1}});

i2 : Q=convexHull(matrix{{0,2}});

i3 : C=cayley(P,Q)

o3 = C

o3 : Polyhedron

i4 : vertices C

o4 = | 0 1 0 2 |
     | 0 0 1 1 |

              2       4
o4 : Matrix QQ  <-- QQ

i5 : C=cayley(P,Q,3)

o5 = C

o5 : Polyhedron

i6 : vertices C

o6 = | 0 1 0 2 |
     | 0 0 3 3 |

              2       4
o6 : Matrix QQ  <-- QQ

i7 : C=cayley({P,Q,Q,P,P},2)

o7 = C

o7 : Polyhedron

i8 : vertices C

o8 = | 0 1 0 2 0 2 0 1 0 1 |
     | 0 0 2 2 0 0 0 0 0 0 |
     | 0 0 0 0 2 2 0 0 0 0 |
     | 0 0 0 0 0 0 2 2 0 0 |
     | 0 0 0 0 0 0 0 0 2 2 |

              5       10
o8 : Matrix QQ  <-- QQ