Prism product

The prism product is an operation that can be applied on any two polytopes to obtain a new one. It generalizes the notion of a prism, which corresponds to the prism product of a polytope and a dyad. In

When talking specifically about convex polytopes, if we identify each polytope with its interior, the prism product corresponds with the better-known Cartesian product. That is, the prism product of an m-dimensional polytope and an n-dimensional polytope is the set of all points in m + n dimensions whose first m coordinates correspond to a point on the interior on the first polytope, and whose last n coordinates correspond to a point on the interior of the other polytope. Nevertheless, while the Cartesian product is defined only for convex polytopes, the prism product is defined for non-convex and even skew polytopes.

The prism product is notable since the prism product of any two uniform polytopes with the same edge length is always uniform. This leads to the existence of a great many families of uniform polytopes in any given dimension.

Up to symmetry, the prism product is both commutative and associative.