Honeycomb product

The honeycomb product or comb product for short, also known as the topological product, is one of four polytope products along with the prism, tegum and pyramid products. Unlike the other three, the honeycomb product of two polytopes is not guaranteed to be of the same sort. However, the honeycomb product of two euclidean honeycombs is itself an euclidean honeycomb.

Definition
If $$A$$ is an abstract polytope of rank $$n$$ and $$B$$ is an abstract polytope of rank $$m$$, then the honeycomb product is defined to be:

$$A\square B=\left\{(a,b)\mid a\in A, b\in B, a\text{ and }b\text{ are either both maximal, both minimal or neither is maximal or minimal}\right\}$$

with the order:

$$(a,b)\leq_{A\square B}(a',b') \iff a\leq_A a' \land b\leq_B b'$$