Pyraminx
Encyclopedia
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
puzzle similar to the Rubik's Cube
Rubik's Cube
Rubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
. It was invented and patented by Uwe Meffert
Uwe Mèffert
Uwe Mèffert has manufactured and sold mechanical puzzles in the style of Rubik's Cube since the original Cube craze. His first design was the Pyraminx and others include the Megaminx, Skewb and Skewb Diamond...
, and introduced by Tomy Toys of Japan (then the 3rd largest toy company in the world) in 1981. Meffert continues to sell it in his toy shop, Meffert's.
Description
The Pyraminx was first conceived by Uwe Meffert in 1970. He did nothing with his design until 1981 when he first brought it to Hong Kong for production. Uwe is fond of saying had it not been for Erno Rubik's invention of the cube, his Pyraminx would have never been produced.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
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
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. Meffert also produces a similar puzzle called the Tetraminx, which is the same as the Pyraminx except that the trivial tips are removed, turning the puzzle into a truncated tetrahedron
Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.- Area and volume :...
.
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, which is also the number of possible patterns on the Tetraminx. 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:| n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| p | 1 | 8 | 48 | 288 | 1728 | 9896 | 51808 | 220111 | 480467 | 166276 | 2457 | 32 |
Records
The current world record for a single solve of the Pyraminx stands at 1.93 seconds, set by Yohei Oka of Japan at Japan Open 2011. The best average time of 3.43 seconds is held by Oscar Roth Andersen of Denmark, set at the Danish Open 2011.See also
- PyramorphixPyramorphixThe Pyramorphix is a tetrahedral puzzle similar to the Rubik's Cube. It has a total of 8 movable pieces to rearrange, compared to the 20 of the Rubik's cube. Though it looks like a simpler version of the Pyraminx, it is an edge-turning puzzle with the mechanism identical to that of the Pocket...
and Master Pyramorphix, two tetrahedral puzzles which resemble the Pyraminx but are mechanically very different from it - Rubik's cubeRubik's CubeRubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
- SkewbSkewbThe Skewb is a combination puzzle- a mechanical puzzle in the style of Rubik's Cube—invented by Tony Durham and marketed by Uwe Mèffert. Although it is cubical in shape, it differs from Rubik's construction in that its axes of rotation pass through the corners of the cube rather than the centres of...
- Skewb DiamondSkewb DiamondThe Skewb Diamond is an octahedron-shaped puzzle similar to the Rubik's Cube. It has 14 movable pieces which can be rearranged in a total of 138,240 possible combinations. This puzzle is the dual polyhedron of the Skewb.- Description :...
- MegaminxMegaminxThe Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's cube.- History :...
- DogicDogicThe Dogic is an icosahedron-shaped puzzle like the Rubik's cube. The 5 triangles meeting at its tips may be rotated, or 5 entire faces around the tip may be rotated. It has a total of 80 movable pieces to rearrange, compared to the 20 pieces in the Rubik's cube.- History :The Dogic was patented by...
- Combination puzzlesCombination puzzlesA combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. The puzzle is solved by achieving a particular combination starting from a random combination...
External links
- Jaap's Pyraminx and related puzzles page, with solution
- Pyraminx solution from PuzzleSolver
- [ftp://ftp.comlab.ox.ac.uk/pub/Cards/txt/Pyramix.txt A solution to the Pyraminx] by Jonathan BowenJonathan BowenJonathan P. Bowen FBCS FRSA is a British computer scientist. He is Chairman of Museophile Limited, an Emeritus Professor at London South Bank University where he has headed the Centre for Applied Formal Methods, and a Visiting Professor at the University of Westminster...
- An efficient and easy to follow solution favoured by speed solvers