Galois' Professor's Revenge

We prove that the groups associated with the Revenge Cube and the Professor’s Cube can be realized as Galois groups over the rationals.

💡 Research Summary

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The paper entitled “Galois’ Professor’s Revenge” claims to realize the permutation groups associated with three Rubik‑type puzzles—the classic 3×3×3 Rubik’s Cube (denoted R₃), the 4×4×4 “Revenge Cube” (R₄), and the 5×5×5 “Professor’s Cube” (R₅)—as Galois groups over the rational numbers ℚ. The authors begin by recalling that the Rubik’s Cube group R₃ has order
(2^{27}3^{14}5^{3}7^{2}11) and that it is already known to occur as a Galois group (reference