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k-l-lambda / k-l-lambda.github.io

Personal blog.
https://k-l-lambda.github.io
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Cube Rotation Algebra | K.L. #8

Open k-l-lambda opened 3 years ago

k-l-lambda commented 3 years ago

https://k-l-lambda.github.io/2020/02/05/cube-algebra/

In 3D space, an object has 6 × 4 = 24 orthogonal orientations in total. Motivation Canonical Rubik’s Cube solver algorithm1 constructs cube state from face colors and a lot of p

reclark commented 2 years ago

I stumbled upon your page trying to find some leads on the use of Pauli matrices in Rubik's Cube analysis. Really cool stuff you're doing here. I think you're right on-target in your deployment of the quaternions in connection with the 24-element rotation group. There's actually some additional use to be made of the octonions in understanding the 210-element group corresponding to the positional relations among the eight corner pieces.

k-l-lambda commented 2 years ago

@reclark Nice advice. I recently learn about Möbius transformation & C^2 homogeneous coordinates, which seems related to Pauli matrices you mentioned. I think there should be an analytical solution for Rubik's Cube shortest path problem if we find the right math tools, while the current best method is merely based on heuristic searching.