Polytope product

There are four operations on polytopes that are collectively known as the polytope products. These are the pyramid product, the prism product, the tegum product, and the comb product.

When looked at concretely, these may appear as very different constructions. Abstractly however, they're all built using a very similar procedure, which mimics the direct product on posets.

These products are useful tools to describe certain polytopes, or to build new ones with various desirable properties, including regularity or uniformity. They're also of theoretical interest – their automorphism groups in particular have been well-studied.