# Rotatopes: the round and flat shapes

## 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