Pyramid

A pyramid is a polytope constructed by tapering a given polytope (the base) to a point (the apex) along a new dimension. The facets of a pyramid are precisely the base and the pyramids of all of the base's facets.

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

Any orbiform polytope with a circumradius of less than 1 has an orbiform pyramid in the next dimension. If the polytope is also CRF, its pyramid is as well.

The regular simplex of each dimension is the pyramid of the simplex of the previous dimension.

Two pyramids from the same base polytope may be joined to create a bipyramid.

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 distance from its apex to its base’s hyperplane. In 2 and 3 dimensions, this formula simplifies to the familiar formulae for the area of a triangle and the volume of a 3D pyramid, respectively.