The epicycloid is the path traced by a point on the edge of a circle as it rolls without slipping along the edge of another circle. The two circles are not required to be the same size:
             ,,.szF'``         ``'Tux.,,
           ,zZ'``                   ``'Cc,
        ,xX``                           ``Ww,
      .uU`                                 `Nn.
     dy`                                     `qb
    /7                                         VA
   4y                                           \D,
  ,I'                                            `U,
  dp                                              qb
 ,j'                                              `t,
 AV                                                VA
 AV                                   R1           VA
|69                       .________________________96|
 VA                                                AV
 VA                                                AV
 `t,                                              ,j'
  qb                                              dp
  `I,                                            ,U'
   \D                                           4y
    VA                                         /7
     qb                                       dy
      `Nn.                                 .uU`
        `Ww,,                           ,,xX`
           'Cc.,,                   ,,.zZ`
             ``'Tux.,,         ,,.szF'``
             ,.szF'``           ``'Tux.,
           ,z'`                       `'c,
         ,x'`                           `'w,
       .u'`                               `'n.
      dy                                     qb
     /7                                       VA
    4y                                         \D
   ,I'                                          `U,
   dp                                            qb
  ,j'                                            `t,
  AV                                  R2          VA
  69                      ._______________________96
  VA                                              AV
  `t,                                            ,j'
   qb                                            dp
   `I,                                          ,U'
    \D                                         4Y
     VA                                       /7
      qb                                     dy
       `'n.                               .u'`
         `'w,                           ,x'`
           `'c,                       ,z'`
             `'Tux.,,           ,,.szF'`
With the above setup, let t be the angle that circle 1 (having radius R1) has rotated around circle 2 (radius R2). Then the parametric equations for the path a point on the edge of circle 1 traces is:
Note that, if R1=R2, then the shape is a cardioid. (In the above setup, I used R1=25chars, R2=24chars.)