Closest 5d analog to the pentagon

[anderscolingustafson]

While there is no direct analog to the pentagon in 5d, as neither the 600 cell nor the 120 cell can form regular 5d polytopes, I think there could be a semi regular 5d polytope that would have some 600 cell hyper cells and some 5 cell hyper cells. It would be sort of like how it is impossible to have a regular 3d polygon with every side as a hexagon yet it is possible to get a semi regular polygon with some sides that are hexagon so long as some of its sides are pentagons. The 600 cell and the 5 cell both have tetrahedral cells so it might be possible for them to be put together to form a 5d polytope. I could be mistaken about this but I think this might be a close 5d analog of a pentagon even though an exact analog of a 5d pentagon is impossible.

[quickfur]

Depends on what you mean by "analog"... analog means that there are some similarities, but obviously also some differences (since otherwise it'd be identical). The question is, what you want to allow to be different.

For example, Gosset's 8-dimensional E₈ polytope projects onto the 600-cell, and so in a sense it captures some part of the essence of the 600-cell, even though it consists only of simplexes and cross polytopes. (I don't know enough about the other E polytopes in lower dimensions, so I can't say if they are similar enough in 5D to the pentagonal polytopes.)

On the other hand, a 5,5-duoprism in 4D is also a "pentagonal" polytope, even though it's probably not what you have in mind (it consists of 10 pentagonal prisms in two interlocking rings). In 5D, you can make a 120-cell prism or a 600-cell prism.