(Except for the Abstract Polytopes, that are still born).
| Dimension | Convex | Nonconvex | Convex Euclidean tessellations | Convex hyperbolic tessellations | Nonconvex hyperbolic tessellations | Abstract Polytopes |
|---|---|---|---|---|---|---|
| 1 | 1 line segment | 0 | 0 | 0 | 0 | 1 |
| 2 | ∞ polygons | ∞ star polygons | 1 | 1 | 0 | ∞ |
| 3 | 5 Platonic solids | 4 Kepler-Poinsot solids | 3 tilings | ∞ | ∞ | ∞ |
| 4 | 6 convex polychora | 10 Schläfli-Hess polychora | 1 honeycomb | 4 | 0 | ∞ |
| 5 | 3 convex 5-polytopes | 0 nonconvex 5-polytopes | 3 tessellations | 5 | 4 | ∞ |
| 6+ | 3 | 0 | 1 | 0 | 0 |
Taking at the periodic table of categories (http://ncatlab.org/nlab/show/periodic+table)
It seems to fit the pattern perfectly at 3-Categories.
What other things exist that are 3-Categories?
