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 1. Number of regular polytopes per dimension.
| Dimension | Count |
|---|---|
| 2 | Infinite |
| 3 | 5 |
| 4 | 6 |
| >4 | 3 |
The cool thing is that the 3 that exist in 5+ dimensions are all of one of the three families:Then, the 2 3D missing ones have 4D analogues and the sixth one in 4D does not have a 3D analogue: the 24-cell. Yes, this is the kind of irregular stuff Ciro Santilli lives for.
- Regular polytope | 5, 390, 5
- Polytope | 37, 472, 23
- Geometry | 0, 7k, 118
- Mathematics | 17, 28k, 633
- Ciro Santilli's Homepage | 262, 218k, 4k
- Classification | 107
- Platonic solid | 45
- The beauty of mathematics | 391, 832, 8