Plato is lifeless starting at 6 dimensions I

Although there are many interesting structures with more than 5 dimensions, regular polyhedra are lifeless:

(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?