A polynomial with Rubik’s cube symmetry

Rubik’s Cube is a well-known combination puzzle that was invented by Ernő Rubik in 1974. What makes the cube interesting, both as a puzzle and as a mathematical object, is the enormous amount of symmetry it has. The puzzle can be permuted in approximately 43 quintillion (4.3×10¹⁹) ways, and a stack of this many cubes would form a tower 261 light years h…