Description
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 = P
o1 : Polyhedron
|
i2 : Q = bipyramid P
Compute barycenter.
Compute barycenter done.
o2 = Q
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
|