Description
The
bipyramid over a
Polyhedron in nspace is constructed by embedding the Polyhedron into (n+1)space, computing the barycentre of the vertices, which is a point in the relative interior, and taking the convex hull of the embedded Polyhedron and the barycentre
x {+/ 1}.
As an example, we construct the octahedron as the bipyramid over the square (see
hypercube).
i1 : P = hypercube 2
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron

i2 : Q = bipyramid P
o2 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 8
number of rays => 0
number of vertices => 6
o2 : Polyhedron

i3 : vertices Q
o3 =  1 1 1 1 0 0 
 1 1 1 1 0 0 
 0 0 0 0 1 1 
3 6
o3 : Matrix QQ < QQ
