Magic Polyhedrons
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.
Twisty Polyhedra by Aditya R M
misc
magic cube books
There are lots books on Rubik cube. rubiks cube book
Two old books I've read in early 1990s are
- Handbook of Cubik Math by D Singmaster et al. Buy at amazon
- Rubik's Cubic Compendium by E Rubik et al. Buy at amazon
I liked the Singmaster one better.
Magic Polyhedrons (David Byrden)
Puzzler
http://www.mud.ca/puzzler/puzzler.html
(2003-07, 2006-09)
Windows
Puzzler is a Windows program by Noel Dilabough. Puzzler plays all types of magic polyhedrons. Puzzler plays some 20 non-trivial variations of magic polyhedrons, including the five platonic solids with different cuts. The program is great, unique, but the interface is very bad. Extremely frustrating to use. Puzzler is a shareware.
MagicCube4D
http://www.superliminal.com/cube/cube.htm. () Windows Linux Java
MagicCube4D by Don Hatch and Melinda Green. It plays 4-dimensional Magic Cube. It also maintains record of the world's first solvers and a solution database. The source code is also available.
4DRubikCube
4DRubikCube by Ishihama Yoshiaki is a 2x2x2x2 magic cube simulator.