by quickfur » Thu May 27, 2010 3:33 am
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.