Wolfram Research
Wolfram Math World: Epicycloid
Shows how to graph them and also derives the polar equations from the parametric equation. The site then defines a few special Epiycloids. Includes a definition, formulas, graphs, video, and links to related topics.
Wolfram Research
Wolfram Math World: Epicycloid1 Cusped
This is a brief page explaining the special epicycloid with one cusp. If you are not yet familiar with the epicycloid, there is a link to help you become familiar.