A *duoprism* is a polytope
that can be expressed as the Cartesian product of two polytopes (each of dimension $\ge 2$).
Four-dimensional duoprisms in particular have been studied:
$$P \times Q = \{ (x_1,x_2,x_3,x_4) \;\mid\; (x_1,x_2) \in P,\; (x_3,x_4) \in Q \} \;,$$
where $P$ and $Q$ are $2$-dimensional polygons.

All the literature I've seen assumes $P$ and $Q$ are convex polygons. For example, here is a net for the product of a square and a regular hexagon:

^{ (Image from Wikipedia page.) }

. Does anyone know of any investigations or uses of duoprisms in which either or both of $P$ and $Q$ are nonconvex polygons?Q