In 4 dimensions we have a total of 6 regular polytopes including the 120-cell, the 600-cell and the 24-cell.

Such groups are often named by the regular polytopes they generate.

There are three series of regular polytopes in all dimensions.

In five or more dimensions, only three regular polytopes exist.

In four dimensions, there are three special regular polytopes, the 24-cell, the 120-cell, and the 600-cell.

Harder still to imagine are the more modern abstract regular polytopes such as the 57-cell or the 11-cell.

In reality, regular polytopes are just very special cases.

Descriptions of these may be found in the List of regular polytopes.

There are no nonconvex regular polytopes of 5 or more dimensions.

In geometry, a bitruncation is an operation on regular polytopes.