# Rotatopes: the round and flat shapes

« Site Map « Shapes of the dimensions

## Last revised 2003-03-16

There is a set of symmetrical shapes that can be constructed from rotations and extensions of lower dimensional shapes. These are called rotatopes, which is a compound from Latin *rota* 'wheel' + -*tope* akin to *polytope*. Two-dimensional rotatopes are called rotagons, and include the square and circle. The square is the extension of a line, and the circle is the rotation of a line. Three-dimensional rotatopes are called rotahedra, and three such shapes are possible. The cube is the extension of a square and the sphere is the rotation of a circle. The cylinder can be constructed in two ways - by extending a circle or rotating a square. Four-dimensional rotatopes are called rotachora, and five such shapes exist. The properties of all of these shapes are described in the three sections below.

- Rotagons (2d shapes) -
**square**, **circle**
- Rotahedra (3d shapes) -
**cube**, **cylinder**, **sphere**
- Rotachora (4d shapes) -
**tetracube**, **cubinder**, **duocylinder**, **spherinder**, **glome**

« Site Map « Shapes of the dimensions