The Rubik's Groups of Polyhedra
Corinna Venezia, New York University
Advisor: Lee Stemkoski, Adelphi University
January 2014
Advisor: Lee Stemkoski, Adelphi University
January 2014
Any convex polyhedron can be subdivided in such a way as to create a configuration puzzle in the style of a Rubik's cube. The set of permutations of the puzzle that can be attained by rotations of faces yields a group. When two polyhedra are dual to eachother, there is a sequence of truncations that can be used to transform one polyhedron into the other. We determine the Rubik groups of polyhedra in these sequences, namely the cube and the octahedron, and show how geometric relationships between them are illustrated by algebraic relationships between the corresponding groups.