Magic Polyhedrons

Xah Lee, 2012-03-03

My favorite type of physical puzzles are the Rubik-type puzzles called Magic Polyhedrons. These puzzles screams: “group theory” and “combinatorics”!

www.mefferts.com sells many magic polyhedrons. I bought about 7 varieties from them in 2001.

A magic polyhedron type of puzzle is essentially defined by the cuts and the solid it cuts into. The cuts defines the mathematical essence of the puzzle, while the solid shape gives the puzzle a flavor. Same cuts can be applied to different solids, yet still resulting the same puzzle mathematically. For example, a tic-tac-toe cut applied to a cube results the Rubic's Cube, and appling it to a sphere results a Rubic Ball. The same tic-tac-toe cut can be applied to octahedron for example.

There are abundant literatures on Rubik cube. Two “oldish” books I've read in early 1990s are Handbook of Cubik Math by D Singmaster et al. amazon. And Rubik's Cubic Compendium by E Rubik et al. amazon. I liked the first one better. Both are fairly popular.

Cubes

Tetrahedrons

Dodecahedron

misc

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For software versions of magic polyhedrons, see: Great Math Programs on Puzzles.