Classification of regular polytopes
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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:
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.