A parametric representation of a Klein bottle, with 'little' radius (the radius of the tube) R1 and 'big' radius (the radius of the loop the tube makes) R2, is as follows:
x = (R1 * cos(t))
y = (R1 * sin(t) * sin(u / 2))
z = ((R2 * cos(u)) + (R1 * sin(t) * cos(u / 2)))
w = (R2 * sin(u))
(0 ≤ u ≤ (2 * π))
(0 ≤ t ≤ (2 * π))
The parameterisation also works with the intervals:
(0 ≤ u ≤ (4 * π))
(0 ≤ t ≤ π)
To make a 3D model, add the w value to the y-coordinate, this will make the shape a bit clearer.