pyramid -- computes the pyramid over a polyhedron

Synopsis

• Usage:

  Q = pyramid P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • Q, a convex polyhedron

Description

pyramid takes the polyhedron P with ambient dimension n and embeds it into QQ^(n+1) on height 0 with respect to the new last variable. Then it computes the convex hull of the embedded P and the point (0,...,0,1).

i1 : P = hypercube 2

o1 = P

o1 : Polyhedron

i2 : Q = pyramid P

o2 = Q

o2 : Polyhedron

i3 : vertices Q

o3 = | -1 1  -1 1 0 |
     | -1 -1 1  1 0 |
     | 0  0  0  0 1 |

              3        5
o3 : Matrix QQ  <--- QQ