Abstract
This poster examines the physical 2x2x2x2, a hand-held realization of a 4-dimensional Rubik’s Cube invented by Melinda Green. Unlike most higher-dimensional twisty puzzles, which exist only as software simulations, this puzzle provides a physical model for exploring 4-dimensional rotation, symmetry, and solving methods. The poster introduces the structure of the puzzle, its canonical move system, and several algebraic ideas that help explain how scrambling and solving work.
From a mathematical perspective, the puzzle can be studied using group actions, commutators, conjugation, and combinatorial counting. In particular, the number of reachable states depends on corner permutations, corner orientations, parity restrictions, twist constraints, and rotational symmetries of the tesseract, yielding approximately 3.36 x 1027 distinct states. Alongside this mathematical framework, the project highlights the puzzle as both a recreational object and a concrete setting for visualizing abstract mathematics.
Faculty Advisor
Dr. Soumya Bhoumik
Department/Program
Math
Submission Type
in-person poster
Date
4-8-2026
Rights
Copyright the Author(s)
Recommended Citation
Moon, Eric J.
(2026)
"A 4-Dimensional Rubik’s Cube You Can Hold: How It’s Possible and the Math Behind It,"
SACAD: Scholarly Activities: Vol. 2026, Article 39.
Available at:
https://scholars.fhsu.edu/sacad/vol2026/iss2026/39
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons
