Tegum

A bipyramid is a polytope constructed by joining together two pyramids of a given polytope by their common base. The facets of a bipyramid are two pyramids for each of the base's facets. Note that the bipyramid from a given base polytope does not contain it as a facet.

The bipyramid operator is a special case of the more general tegum product. Particularly, a bipyramid built from a polytope P is the same as the tegum product of P and a dyad. Due to that, bipyramids are also called tegums.

Any orbiform CRF polytope with a circumradius of less than 1 has a CRF bipyramid in the next dimension. However, this bipyramid generally does not have a unique circumradius.

Any polytope whose facets are all congruent has a bipyramid with the same property.

The regular orthoplex of each dimension is the bipyramid of the orthoplex of the previous dimension.

The dual of a bipyramid is a prism based on the dual polytope.

Volume
The hypervolume of a pyramid in n dimensions can be calculated with the formula:


 * V = Ah / n,

where A is the hypervolume of the pyramid's base, and h is the pyramid’s height, the sum of the distances from its apices to its base’s hyperplane.