Umbilic Torus

An umbilic Torus

You can spin the above object by left-dragging on the object itself. Holding the shift-key will have other effects.

The equations for the umbilic torus can be given parametrically by:

x = \sin{u}\left[7+\cos\left(\frac{u}{3}-2v\right) + 2\cos\left(\frac{u}{3} + v \right)\right]

y = \cos{u}\left[7+\cos\left(\frac{u}{3}-2v\right) + 2\cos\left(\frac{u}{3} + v \right)\right]

z = \sin\left(\frac{u}{3}-2v\right)+ 2\sin\left(\frac{u}{3}+2v\right)