A 1-cusped epicycloid has 
, so 
. The radius measured from the center of the large circle
for a 1-cusped epicycloid is given by epicycloid equation
(◇) with 
so
 |  | ![(a^2)/(n^2)[(n^2+2n+2)-2(n+1)cos(nphi)]](/images/equations/Epicycloid1-Cusped/Inline6.svg) |
(1)
|
 |  | ![a^2[(1^2+2·1+2)-2(1+1)cos(1·phi)]](/images/equations/Epicycloid1-Cusped/Inline9.svg) |
(2)
|
 |  |  |
(3)
|
 |
(4)
|
and
 |
(5)
|
The 1-cusped epicycloid is just an offset cardioid.
