Overview
This table shows a summary of regular polytope counts by dimension.
| Dimension | Convex | Nonconvex | Convex Euclidean tessellations |
Convex hyperbolic tessellations |
Nonconvex hyperbolic tessellations |
Hyperbolic Tessellations with infinite cells and/or vertex figures |
Abstract Polytopes |
|---|---|---|---|---|---|---|---|
| 1 | 1 line segment | 0 | 1 | 0 | 0 | 0 | 1 |
| 2 | ∞ polygons | ∞ star polygons | 1 | 1 | 0 | 0 | ∞ |
| 3 | 5 Platonic solids | 4 Kepler–Poinsot solids | 3 tilings | ∞ | ∞ | 0 | ∞ |
| 4 | 6 convex polychora | 10 Schläfli–Hess polychora | 1 honeycomb | 4 | 0 | 11 | ∞ |
| 5 | 3 convex 5-polytopes | 0 | 3 tessellations | 5 | 4 | 2 | ∞ |
| 6 | 3 convex 6-polytopes | 0 | 1 tessellation | 0 | 0 | 5 | ∞ |
| 7+ | 3 | 0 | 1 | 0 | 0 | 0 | ∞ |
There are no nonconvex Euclidean tessellations in any number of dimensions.
Read more about this topic: List Of Regular Polytopes