Pyraminx Cube: The Pyraminx was first made by Mèffert in the year 1970. He did nothing with his design until 1981 when he first took it to Hong Kong for production. Uwe likes to say that if it hadn’t been for Ernő Rubik’s invention of the cube, his Pyraminx would never have been produced.
Pyraminx is a straight-shaped puzzle with 4 axial pieces, 6 edge pieces, and 4 trivial points. It can be twisted along your cuts to market your pieces. Axial parts are octahedral, and can only rotate around the axis to which they are attached The six edges can be placed in 6!
because they can be twisted independently of all the other pieces, making them trivial to put them in the resolved position. Meffert also produces a similar puzzle called Tetraminx, which is the same as Pyraminx, except that the mundane edges are removed, turning the puzzle into a truncated tetrahedron.
The purpose of Pyraminx is to mix colors and then return them to their original settings.
The 4 tips can be easily rotated to align with the axial piece to which they respectively match, and the axial pieces can also be easily rotated so that their colors align with each other. This leaves only the 6 pieces on the board as a real challenge to the puzzle. They can be solved by repeatedly applying two 4-twist sequences, which are mirror versions of each other. These sequences switch 3 pieces of the board at a time and change their orientation differently, so a combination of the two sequences is enough to solve the puzzle. However, more efficient solutions (requiring fewer total twists) are generally available (see below).
The twist of an axial part is independent of the other three, as in the case of the tips. The six edges can be placed in many positions and inverted 25 ways, taking parity into account. Multiplying by a factor of 38 for the axial parts gives 75,582,720 possible positions. However, setting the mundane hints to the correct positions reduces the possibilities to 933,120, which is also the number of possible patterns in Tetraminx. Defining the axial pieces also reduces the number to just 11,520, making this a very easy puzzle to solve.
There are 2 general methods for solving Pyraminx, V-First – where you solve one level except one edge before finishing the puzzle, and Top-First – where you solve the top of the puzzle before solving the rest. None of the approaches to solving the Pyraminx cube is a great approach than the other one, Moreover, the V-First method I like to adapt when solving as it is much more easier to understand and intuitive rather than the Top-First approach. Therefore, in this guide, I will provide tips on more advanced V-Firsts solution techniques (as well as more general advice).
This guide is a tip, tricks, and advice that will improve your Pyraminx play and solution. I will mainly deal with L4E resolution, as by reading this guide you should already have a good understanding of LBL resolution.
L4E (last 4 edges) is an advanced “V” method mainly used for sub-5 and higher resolution. Instead of creating a complete layer as you would with the LBL (Layer By Layer) method; L4E consists of creating a “V” (level minus one edge) before using an intuitive (or learned) algorithm to solve the remaining 4 edges, hence the method name. This method has much more “speed potential” than the LBL method, such as looking for just a “V” during an inspection rather than an entire layer; you are able to look ahead and influence the L4E case, offering more opportunities for a more fluid and advanced solution.