The bipyramid over a Polyhedron in n-space 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 |
The object bipyramid is a method function.