Setup

n = 3 (slider from 2 to 20, step 1)
p = 2.67 (slider from 0 to 5, step 0.01)
r = 2.53 (slider from 0 to 10, step 0.01)
R = 3.47 (slider from 0 to 10, step 0.01)
t = 4.12 (slider from 0 to 6.283185307179586, step 0.01)
cx(x, y) = ((R - (r * cos(x))) * cos((p * x) + y))
cy(x, y) = ((R - (r * cos(x))) * sin((p * x) + y))
cz(x, y) = (r * sin(x))
Lm = Sequence(k, k, 0, (2 * π), (2 * π / n))
L_1 = Zip(Surface[cx(u, v), cy(u, v), cz(u, v), u, 0, (2 * π), v, m + π / n, m + (2 * π / n)], m, Lm)
R_1 = Rotate(L_1, (-t), zAxis)