List of mathematical shapes

This table shows a summary of regular polytope counts by dimension.

For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.

The classical convex polytopes may be considered tessellations, or tilings, of spherical space.

Tessellations of euclidean and hyperbolic space may also be considered regular polytopes.

There is only one polytope in 1 dimension, whose boundaries are the two endpoints of a line segment, represented by the empty Schläfli symbol {}.