Pyraminx

The Pyraminx is a tetrahedron-shaped puzzle similar to the Rubik's Cube. It was invented and patented by Uwe Meffert, and introduced by Tomy Toys of Japan (then the 3rd largest toy company in the world) in 1981. [http://www.mefferts.com/puzzles-pyraminx-kokonotsu.htm] Meffert continues to sell it in his toy shop, [http://www.mefferts.com Meffert's] .

Description

The Pyraminx is a puzzle in the shape of a tetrahedron, divided into 4 axial pieces, 6 edge pieces, and 4 trivial tips. It can be twisted along its cuts to permute its pieces. The axial pieces are octahedral in shape, although this is not immediately obvious, and can only rotate around the axis they are attached to. The 6 edge pieces can be freely permuted. The trivial tips are so called because they can be twisted independently of all other pieces, making them trivial to place in solved position.

The purpose of the Pyraminx is to scramble the colors, and then restore them to their original configuration.

The 4 trivial tips can be trivially rotated to line up with the axial piece which they are respectively attached to; and the axial pieces are also easily rotated so that their colors line up with each other. This leaves only the 6 edge pieces as a real challenge to the puzzle. They can be solved by repeatedly applying two 4-twist sequences, which are mirror-image versions of each other. These sequences permute 3 edge pieces at a time, and change their orientation differently, so that a combination of both sequences is sufficient to solve the puzzle. However, more efficient solutions (requiring a smaller total number of twists) are generally available (see below).

The twist of any axial piece is independent of the other three, as is the case with the tips. The six edges can be placed in 6!/2 positions and flipped in 2⁵ ways, accounting for parity. Multiplying this by the 3⁸ factor for the axial pieces gives 75,582,720 possible positions. However, setting the trivial tips to the right positions reduces the possibilities to 933,120 and setting the axial pieces as well reduces the figure to only 11,520, making this a rather simple puzzle to solve.

Optimal solutions

The maximum number of twists required to solve the Pyraminx is 11. There are 933,120 different positions (disregarding rotation of the trivial tips), a number that is sufficiently small to allow a computer search for optimal solutions. The table below summarizes the result of such a search, stating the number "p" of positions that require "n" twists to solve the Pyraminx:

Records

The current world record for a single solve of the Pyraminx stands at 2.83 seconds, set by Tomasz Kiedrowicz at the Gdansk Open competition (Poland) on February 24, 2008.

See also

*Pocket cube
*Rubik's cube
*Skewb Diamond
*Megaminx
*Dogic
*Combination puzzles

External links

* [http://www.geocities.com/jaapsch/puzzles/pyraminx.htm Jaap's Pyraminx and related puzzles page, with solution]
* [http://www.puzzlesolver.com/puzzle.php?id=28 Pyraminx solution] from [http://www.puzzlesolver.com/ PuzzleSolver]
* [ftp://ftp.comlab.ox.ac.uk/pub/Cards/txt/Pyramix.txt A solution to the Pyraminx] by Jonathan Bowen
* [http://www.geocities.com/rubiks_galaxia/PyraSol.html An efficient and easy to follow solution favoured by speed solvers]
* [http://www.mud.ca/puzzler/JPuzzler/JPuzzler.html Online Pyraminx]