Pyramid

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

Any CRF polytope with a circumradius of less than 1 has a CRF pyramid in the next dimension.

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

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


 * Vn = A*h / n

where A is the hypervolume of the pyramid's base in n-1 dimensions, and h is the height of the pyramid in the nth dimension.

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.