# Rotatope (EntityClass, 7)

### From Higher Dimensions Database

A **rotatope** is the Cartesian product of a set of hyperspheres. Rotatopes were invented by Jonathan Bowers and the name was coined by Garrett Jones in 2003. The number of rotatopes in *n* dimensions is simply the partition function of *n*. The cardinal cross sections of any rotatope are always rotatopes of one dimension lower. Extruding a rotatope or lathing it around a cardinal axis will always produce a rotatope of one dimension higher. In fact, all rotatopes can be produced by extruding or lathing the point multiple times. Rotatopes can be written in either tapertopic notation, toratopic notation or bracket notation as rotatopes are included in all three of these sets. They can also be written in SSC2, SSCN and CSG notation.

Rotatopes of two dimensions or higher also function as expanded rotatopes: a rotatope which is (at its minimal frame) homeomorphic to a set of toratopes of lower or equal dimension. These minimal frame rotatopes have unique homology groups.