There are 933,120 different positions (disregarding the trivial rotation of the tips), a number that is sufficiently small to allow a computer search for optimal solutions. The maximum number of twists required to solve the Pyraminx is 11. Setting the axial pieces as well reduces the figure to only 11,520, making this a rather simple puzzle to solve. 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. Multiplying this by the 3 8 factor for the axial pieces gives 75,582,720 possible positions. The six edges can be placed in 6!/2 positions and flipped in 2 5 ways, accounting for parity. The twist of any axial piece is independent of the other three, as is the case with the tips. However, more efficient solutions (requiring a smaller total number of twists) are generally available (see below). 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. They can be solved by repeatedly applying two 4-twist sequences, which are mirror-image versions of each other. This leaves only the 6 edge pieces as a real challenge to the puzzle.
The 4 trivial tips can be easily rotated to line up with the axial piece they are respectively attached to, and the axial pieces are also easily rotated so that their colors line up with each other. The purpose of the Pyraminx is to scramble the colors, and then restore them to their original configuration. 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 trivial tips are so called because they can be twisted independently of all other pieces, making them trivial to place in solved position. The 6 edge pieces can be freely permuted. The axial pieces are octahedral in shape, although this is not immediately obvious, and can only rotate around the axis they are attached to. It can be twisted along its cuts to permute its pieces.
The Pyraminx is a puzzle in the shape of a regular tetrahedron, divided into 4 axial pieces, 6 edge pieces, and 4 trivial tips.
Somewhat earlier (for 40 days) in the Soviet Union, the chief technologist of the Kishinev Tractor Plant, Alexander Alexandrovich Ordynets, filed his application for an invention (patent SU980739 dated, with the filing date 02/18/81), because of that, in Russia many people call puzzle "Молдавская пирамидка" (moldavian pyramid). Uwe is fond of saying had it not been for Ernő Rubik's invention of the cube, his Pyraminx would have never been produced. He did nothing with his design until 1981 when he applied for a patent on 27/03 ( EP0042695 on 12/30/81) and brought it to Hong Kong for production. The Pyraminx was first conceived by Mèffert in 1970.
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