There is another product (or something like a product), involving digons.

For two abstract polytopes A and B, let A'=A\{body(A)} and B'=B\{nulloid(B)}, and take the (disjoint) union C=A'∪B'. Define a partial order on C in terms of the partial orders on A and B, thus: a₁≤a₂ in C if and only if a₁≤a₂ in A'; b₁≤b₂ in C if and only if b₁≤b₂ in B'; and a≤b and not b≤a (where a is anything in A', and b is anything in B'). So, each vertex of B takes the place of the body of A.

The result C is always a polytope, if A and B are greater than (-1)-polytopes. The dimension is dim(C)=dim(A)+dim(B). Every [dim(A)-2, dim(A)+1]-subpolytope in C is a digon.

If B is a 1-polytope, then C is a ditope. If A is a 1-polytope, then C is a hosotope.