This table was primarily motivated by wanting to understand how Yoshinobu Miyamoto's torus template was created. I initially toyed with the idea of solving this problem mathematically but quickly realized that analytically slicing an elliptical torus with 8 unique planes is a non-trivial problem.
Therefore, I used SketchUp (a free tool) to approximately solve the problem with sufficient accuracy. What follows is an elliptic torus sliced via 8 planes such that all planes intersect at a single point occuring at the center of the elliptic torus:
Using SketchUp's Section Plane command allows one to see the Villarceau ellipses (which are similar to Villarceau circles):
This section plane slice (revealing the Villarceau ellipses) can then be used to create "male" and "female" templates suitable for printing:
As with the Copper Torus, 16 such slices (8 male and 8 female) were used to create the table:
