{tag=Classification (mathematics)}
{wiki=Regular_polytope\#Classification_and_description}

The 3D regular convex polyhedrons are super famous, have the name: <Platonic solid>, and have been known since antiquity. In particular, there are only 5 of them.

The counts per dimension are:
\Table[
|| Dimension
|| Count

| 2
| Infinite

| 3
| 5

| 4
| 6

| \>4
| 3
]
{title=Number of regular polytopes per dimension}

The cool thing is that the 3 that exist in 5+ dimensions are all of one of the three families:
* <simplex>
* <hypercube>
* <cross polytope>
Then, the 2 3D missing ones have 4D analogues and the sixth one in 4D does not have a 3D analogue: https://en.wikipedia.org/wiki/24-cell[the 24-cell]. Yes, this is the kind of irregular stuff <Ciro Santilli> lives <the beauty of mathematics>[for].


Classification of regular polytopes

ID: classification-of-regular-polytopes