A parametric representation of a Klein bottle, with 'little' radius (the radius of the tube) `R`_{1} and 'big' radius (the radius of the loop the tube makes) `R`_{2}, is as follows:

`x` = (`R`_{1} * cos(`t`))

`y` = (`R`_{1} * sin(`t`) * sin(`u` / 2))

`z` = ((`R`_{2} * cos(`u`)) + (`R`_{1} * sin(`t`) * cos(`u` / 2)))

`w` = (`R`_{2} * 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.