# Tegum

**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[edit | edit source]

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.