Some animations accompanying a work in progress investigating the geometry of the BiDisk.
A parameterization of the 3-Sphere as the union of 2 solid tori glued along their boundaries. The parameters for the 2 tori are:
The radial level sets
The θ1 and φ2 level sets
The θ2 and φ1 level sets
The boundary of the flats fixed by the 444 triangle group and their images under 5 iterates of that group