Magic Polyhedrons

By Xah Lee. Date: . Last updated: .

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.

Kawai MP9000 piano dodecahedron

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

Twisty Polyhedra by Aditya R M 2023-07-23
Twisty Polyhedra by Aditya R M 2023-07-23
cube 5x5x5-professors cube
magic cube Magic Cube 4x4x4 magic cube 5x5x5
pyramorphix pyramorphix-scrambled
Pyraminx solved Pyraminx-3 Pyraminx-Tetraminx
magic pyramid
gigaminx mf8
teraminx mf8 976
Tetraminx. Buy at amazon
pentaminx mf8 lf8zb
Pentaminx. It's a mavel, how this is made. That by itself is a great math puzzle. Buy at amazon
lanlan curvy copter puzzle d270d
LanLan Curvy Copter Puzzle Buy at amazon
mirror cube 0b01h
Mirror Cube


Skewbdiamond skewb-cube skewb-diamond Dogic12 skewb-ultimate

magic cube books

There are lots books on Rubik cube. rubiks cube book

Two old books I've read in early 1990s are

I liked the Singmaster one better.

magic 17 cube  2019-03-05 48bxw
magic 17 cube 2019-03-05

Magic Polyhedrons (David Byrden)

David Byrden's java applet David Byrden's java applet
David Byrden's magic polyhedron Java applets.


puzzler (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 () 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.


4DRubicCube Mac OS 9 Windows Java

4DRubikCube by Ishihama Yoshiaki is a 2x2x2x2 magic cube simulator.