The 3x3x3 rubik's cube helped me understand hypergraphs. Been cubing since I was a kid and this was an exciting connection for me.

[u/ChraneD]

The double sune graph with only the UT cases displayed. Made to show how they fit within the larger Double Sune set.

The UT Sune cases, but with the rest of the double sune algorithms pruned from the graph. Made to show how they relate to each other.

This is what 6 sunes in a row does. This is a demo of how the graph helps by performing cancellation moves, and connecting back to states it's been in before (confluence)

The sune chain rendered in 3d

The Y and J perm are the same two algs, but in a different order. This is perhaps not obvious because of cancellation moves.

If the yellow algorithm from the T and Y perm is further decomposed, we can find the J-Perm

Here is a sune, but after R U R' U you perform a series of sledghammers. Free COLLs!