Pyraminx

The Pyraminx (/ˈpɪrəmɪŋks/) is a regular tetrahedron puzzle in the style of Rubik's Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubik's Cube by Erno Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy company in the world) in 1981.[1]

Description

The Pyraminx was first conceived by Mèffert 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 regular 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. 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.

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

The 4 trivial tips can be easily 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 012 3 4 5 6 7 8 9 10 11
p 18482881728989651808220111480467166276245732

Records

Solving pyraminx in a competition. Andreas Pung at Estonian Open 2011.

The current world record for a single solve of the Pyraminx stands at 1.32 seconds, set by Drew Brads at the Lexington Fall 2015. He also holds the fastest average of 5 (with the fastest and slowest solve disregarded) with 2.14 seconds at US Nationals 2016.[2][3]

Methods

There are many methods for solving a Pyraminx. They can be split up into two groups.

1) V first- In these methods, two or three edges, and not a side, is solved first, and a set of algorithms, also called LL algs (last layer algs), are given to solve the remaining puzzle.

2) Top first methods- In these methods a block on the top, which is three edges around a corner, is solved first and the remaining is solved using a set of algorithms.

Common V first methods-

a) Layer by Layer - In this method a face with all edges oriented in the right spot aka a layer is solved and then the remaining puzzle is solved using 5 algorithms particularly for this method.

b) L4E- L4E or last 4 edges is very similar to Layer by Layer. The only difference is that TWO edges are solved around three Centers, and the rest is done by a set of algorithms

c) Intuitive L4E- A method similar to the L4E, as the name suggests, in which lots of visualization is required. The set of algorithms mentioned in the previous method are not memorized. Instead, cubers intuitively solve each case by anticipating the movement of pieces. This is the most advanced V first method

Common top first methods-

a) One Flip- This method uses two edges around one centre solved and the third edge flipped. There are a total of six cases after this step, for which algorithms are memorized and executed. The third step involves using a common set of algorithms for ALL top first methods, also called Keyhole last layer, which involves 5 algorithms, four of them being the mirrors of each other.

b) Keyhole- This method uses two edges in the right place around one centre, and the third edge does not match any color of the edge i.e. it is not in the right place OR flipped. The centers of the fourth color are then solved USING the non oriented edge aka keyhole. The last step is solved using Keyhole last layer algs

c) OKA- In this method, One edge is oriented around two edges in the wrong place, but one of the edges that is in the wrong place belongs to the block itself. The last edge is found on the bottom layer and a very simple algorithm is executed to get it in the right place, followed by keyhole last layer algs.

Some other common top first methods are WO and Nutella

Professional Pyraminxers like Drew Brads usually learn all methods, and while observing a case, decide which method best suits that case

Variations

A solved Tetraminx.

There are a few variations of the puzzle. The most popular ones are the Professor Pyraminx, which is a higher-order version of the Pyraminx, and the Tetraminx, equivalent to the Pyraminx but without the tips.

See also

References

  1. ↑ http://www.mefferts.com/puzzles-pyraminx-kokonotsu.htm
  2. ↑ "Pyraminx - Official World Records (Single and Average)". World Cube Association. Retrieved 4 August 2016.
  3. ↑ "Drew Brads - Official Results". World Cube Association. Retrieved 4 August 2016.
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