Magic Polyhedrons

By Xah Lee. Date: . Last updated: .
Kawai MP9000 piano dodecahedron
magic dodecahedron.

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

I bought about 7 varieties from mefferts puzzles 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 or other shapes.

Modern ones are stickerless. This is a improvement, because you don't have to worry about stickers falling out or dealing with the glue leaking on the edge of the stickers.

magic cube 3x3x3 newisland structure torpedoes stickerless 90752
Magic cube 3x3x3. magic cube
magic cube 4x4x4 cube
“Magic Cube 4x4x4” Buy at amazon
cube 5x5x5-professors cube
magic cube 5x5x5. Buy at amazon
pyramorphix pyramorphix-scrambled
Magic pyramid 2.
Pyraminx  Mastermorphix Shengshou stickerless Pyraminx  Mastermorphix Shengshou stickerless twisted
Buy at amazon
Pyraminx solved Pyraminx-4 Pyraminx-3 Pyraminx-Tetraminx
Magic pyramid. magic pyramid
magic dodecahedron Shengshou Megaminx
Megaminx. megaminx
gigaminx mf8
Gigaminx. Buy at amazon
teraminx mf8 976 teraminx mf8 twisted
Tetraminx. Buy at amazon image source
pentaminx mf8
pentaminx. It's a mavel, how this is made. That by itself is a great math puzzle. Buy at amazon


Skewbdiamond skewb-cube skewb-diamond Dogic12 skewb-ultimate

on amazon:

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

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

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