I've just discovered something really fascinating: the existence of a class of 4D zonotopes that consist of identical regular 3D prisms.
Prismic zonotopes
Consider the tetracube with its 8 cells in cell-first perspective projection. This is the "cube-within-a-cube" projection. Let's call the outer cube A, and the inner cube C. Call the upper frustum D and the lower frustum B. The cubes A, B, C, D, form a cycle in the ZW plane. Now consider the 4 side frustums. Let's call these cubes P, Q, R, and S. These form another cycle, in the XY plane. These two cycles are orthogonal.
Now, let's substitute the cubes with, for example, triangular prisms. The ZW cycle can be reduced to a 3-member cycle of triangular prisms, attached to each other by their triangular faces. The XY cycle can likewise be reduced to a 3-member cycle, also attached to each other by their triangular faces. The square faces of the prisms in these two cycles exactly match each other. The result is a closed 4D zonotope made of 6 triangular prisms. These prisms form two 3-member cycles that are interlocked with each other.
We can also do the substitution with other types of prisms, for example, with pentagonal prisms. Then we expand the ZW cycle to include a 5th member. The cycle of 5 square faces of adjacent prisms precisely form a gap that can be filled in by other pentagonal prisms, which will form a 5-member XY cycle. In other words, now we have a prismic zonotope made of 10 pentagonal prisms.
This process actually works with all n-gonal prisms, as long as all edges in the prisms are equal. The result will be a zonotope of 2n prisms. This is fascinating, because all facets of these zonotopes are identical prisms. (The tetracube is just a special case, when square prisms (i.e. cubes) are used.)
Double-torus
Now, what is interesting is when we take the limit of these prisms as n approaches infinity. The limit of the ZW cycle is a circular torus formed by rotating a circle in the XY plane around the ZW plane. The limit of the XY cycle is also a circular torus, formed by rotating a circle in the ZW plane around the XY plane. In other words, this is a "double-torus"-like 4D volume bounded by two torii. (Does anybody know what this object is called, if it does have a name? If not, may I suggest to name this object the 4D double-torus? :-) ) What is fascinating is that, if my intuition is right, this object can roll in two orthogonal planes... which means it can cover the same area as a spherical cylinder. (Alkaline should add this to his collection of rotatopes ;-))
[Update (2005-06-13): I just found out that this shape is in fact the same as the duocylinder.]
Mixed prismic polytopes
The n-gonal prismic zonotopes aren't the only possibilities. We can also mix two different kinds of prisms: for example, we can use cubes in the ZW cycle, but add a 5th cube to it. This produces a cycle of 5 square faces on the sides of the cycle, which can be closed by 4 pentagonal prisms. This will produce a polytope made of 5 cubes and 4 pentagonal prisms.
In general, we can take n m-gonal prisms and m n-gonal prisms and construct analogous polytopes in this way. For example, we can build a polytope from 7 triangular prisms and 3 heptagonal prisms. If n=4, we get the same polytope we would get by extruding an m-gonal prism into 4D. Similarly for m=4. Of course, things are a lot more interesting when neither n and m equal 4. The cool thing about these polytopes is that the gonality of the prisms in one cycle is equal to the number of prisms in the other cycle, and vice versa, so they are completely determined by the two numbers n and m.
Is there a consistent naming convention for these things? (Wendy?) These aren't really prisms in the 4D sense; they are just built from 3D prisms. I was thinking maybe I can name them the "prismic bicycles" ("bicycle" as in bi- + -cycle, for the ZW and XY cycles, not the vehicle :-)) I like the sound of a "5,6-prismic bicycle", or a "7,7-prismic bicycle". :-) In general, the name would be "n,m-prismic bicycle" where n and m are integers greater than 2.
(And I have this inkling that in 6D, we could have tri-cycles... although I'm not sure what the 5D equivalent of prisms would be.)