I’m pretty tired, so maybe that’s why I don’t understand well why a 4D hypercube (two 3D cubes with edges in the 4D plane between each pair of corresponding vertices) has eight total 3D cubes. The hypercube has 16 vertices and 32 lines. I know there are 16 “original” 3D cube edges, but where do the extra 16 come from? Is each of the 8 connections between vertices 2 lines?
Come to think of it, are the vertices points in this case? Or are they lines? Because the hypercube “faces” are 3D cubes. So maybe everything is promoted? Edges are squares and vertices are lines.
So, what are the points, then, if not vertices?
OK, the Wikipedia article says the vertices are still points.
If the two cubes are connected by eight traditional lines, though, how would that produce the six additional cubes? I guess it’s a matter of finding adjacent squares in the network of lines.
Welp, I’m not sure I’ll understand this any better when I’m rested, but I do know that if I were a right-wing politician I would be railing against hypercubes. Incomprehensible wokery that no one wants to hear about!