By Fang Fang. October 18, 2016.
A few years ago I discovered that the dihedral angle of the 600-cell is exactly the same as the relative face rotational angle in the 20-group twist. When I told Klee about this, he had the intuition that this relationship cannot be simply a coincidence. He conjectured that there should be an inverse relationship between the curvature in the 600-cell (which is on a 3-sphere) and the twisting angle in the 20-group twist because they both encode the geometric frustration in the regular tetrahedral packing.
Klee has been very persistent on his conjecture although various scientists, both in and out of our group, have tried but not been able to prove it. Read More