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.
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[edit | edit source]
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.