**PURPOSE: **Visualize the Platonic solids and Kepler's dream
for using them to explain planetary orbits.

**DESCRIPTION: **There are five three-dimensional Platonic solids.
The faces of a Platonic solid are identical regular polygons and all
vertex angles are equal. These solids are:

As illustrated in the accompanying transparency, Kepler spent most of his life assuming that planetary orbits were circular and trying to use Platonic solids to deduce their radii. Only much later, after he gave up his dream, did he discover his true laws for planetary motion. Although Kepler's original dream was a failure, much of the same mathematical/geometrical spirit prevails in our modern attempts to explain the fundamental nature of matter via symmetry, group theory, field theory, the geometry of various higher dimensional manifolds, and string theory.

**SUGGESTIONS: **Pass them around.

**REFERENCES: **(PIRA unknown.)

**EQUIPMENT: **Platonic solids and viewgraph transparency of
Kepler's construction.

**SETUP TIME: **None.