Tegum

A square bipyramid, constructed from a square.

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

The tegum operator is a special case of the more general tegum product. Particularly, a tegum built from a polytope P is the same as the tegum product of P and a dyad.

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

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

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

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

Volume

The hypervolume of a tegum 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.