Rubik's Abstract Polytopes
Giovanni Luca Marchetti
TL;DR
This paper extends the concept of the Rubik's cube to abstract regular polytopes, analyzing the configuration groups of higher-dimensional analogs like the simplex and hypercube.
Contribution
It generalizes Rubik's cube theory to abstract regular polytopes and provides a complete group description for the Rubik's simplex, with insights into the hypercube case.
Findings
Complete group description for the Rubik's simplex
Generalization of Rubik's cube to arbitrary regular polytopes
Sketch of the hypercube case analysis
Abstract
We generalize the Rubik's cube, together with its group of configurations, to any abstract regular polytope. After discussing general aspects, we study the Rubik's simplex of arbitrary dimension and provide a complete description of the associated group. We sketch an analogous argument for the Rubik's hypercube as well.
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Taxonomy
TopicsMathematics and Applications