Nylon

120-Cell

The dodecahedron is well known as the most noble of all Platonic solids, and this projection of its 4D analogue packs in 120 of them, from the outer hull to the tiny central cell. What a deal!

24-Cell

The only 4D regular solid without an analog among the five 3D Platonics, this is clearly in the neighborhood of the cube and octahedron, but not quite like either: a thing unto itself.

Hypercube A

The tesseract, showing 8 cubic faces in its most familiar style. This is a cell-first projection, which in 3D is like a cube drawn with one side squarely facing you. Here in 4D the "front" and "back" are regular cubes, without off angles caused by perspective.

Hypercube B

A vertex-first projection of the same tesseract, in 3D this is like a cube drawn with a corner facing you, so all its faces are shown in perspective. In this style the hull forms a rhombic dodecahedron, I think it's pretty.

16-Cell

The 4D style octahedron with 16 tetrahedral faces, dual to the hypercube. In its native dimension all the tetrahedra are regular, here all but two are skewed by the perspective projection into 3-space.

Simplex

With just 4 cells, the 4D tetrahedron.

600-cell

Lastly the 4D icosahedron: 600 tetrahedral cells with five meeting along each edge, just as in 3D five triangles meet at each vertex.

This projection was carefully chosen to make the model buildable at reasonable size.