Here are some other epicycloids. A hypocycloid is the locus of a point on the circumference of which is rolling around the inside of a fixed circle. The rolling circle better not have to have the same radius as the fixed circle, because if it did, then the resulting figure would just be a point. Epiroulettes An epiroulette , also called an epitrochoid , is like an epicycloid in that one circle is rolling around another circle, but the drawing point need not be exactly on the edge of the rolling circle. The drawing point could instead be inside or outside the circle.
Cardioids are special cases of epiroulettes.
Hyporoulettes A hyporoulette , also called a hypotrochoid , is like an epicycloid in that one circle is rolling inside another circle, but, as you could guess, the drawing point need not be exactly on the edge of the rolling circle. If the drawing point is at the center of the moving circle, the resulting hyporoulette is a circle, but otherwise, it' s a proper ellipse. Here are some in this picture. They are just the epirosettes or hyporosettes passing throught the center of the fixed circle. And some more roses .