I have been spending a lot of time recently thinking about higher dimensional geometry, both flat and curved. I've been lurking this forum and wiki for many years on and off, but since I have fully come back to the topic, I made an account of my own. I was thinking about the duoprisms in six dimensions, that are constructed of polyhedral prisms. I looked around but could not find any content on the idea I had today, so I am posting it here as "duohyperprisms," because I don't know if it has a proper name. In 4D, the most basic duoprisms will be the simplex duoprisms, which are written as 3,3-duoprisms, the Cartesian product of two triangles. In 6D, you can have a 3,3,3,-trioprism, which is the Cartesian product of three triangles, but you can also have the simplex duohyperprism, which is the Cartesian product of two tetrahedra.

I guess because there is so much more possibility in 3D than there is in 2D, you can make a lot of weird but still regular duohyperprisms in 6D, such as the "triangular prism soccer ball" duoprism, which is the Cartesian product of a triangular prism and a truncated icosahedron. It becomes difficult to write out the names in an "m,n-duoprism" format, but I propose the usage of Schläfli symbols in place of m and n. For example, the simplex duohyperprism would be "{3,3},{3,3}-duoprism," and the triangular prism soccer ball duohyperprism would be "t{2,3},t{3,5}-duoprism." Kind of ugly to read, but it's rigorous.

The m,n limit of m,n-duoprisms in 4D is the duocylinder, and the m,n,o limit of m,n,o-trioprisms is the triocylinder. You can't really talk about limits with polyhedra without invoking the infamous apeirogon or apeirohedron, but I think the equivalent idea of m,n-duohyperprisms in 6D would be the "duospherinder." Maybe the real magic happens in 8D, where you can have duoprisms that are Cartesian products of lower dimensional duoprisms.