# Pyraminx

Pyraminx, mixed
Pyraminx during a rotation from the basic position

The Pyraminx is about 6  cm large mechanical puzzle in the form of a regular tetrahedron , which with the principle and construction to Rubik's Cube by Erno Rubik is comparable. This is why the term magic pyramid is also used . Each of the four side surfaces is made up of nine triangular segments, which in the basic position all have the same color on each side. With the internal rotating mechanism, both the side surfaces and the corners can be brought into congruence again by rotating 120 ° around their center. In this way, the moving parts change their position in relation to one another and can be moved to almost any point in the tetrahedron. The aim of the game of patience is usually to bring the Pyraminx from a position in which the colors are mixed back to the ordered basic position.

## history

The German puzzle inventor Uwe Meffert developed the Pyraminx in the late 1970s as part of the great success of the Rubik's Cube. Meffert received a European patent in March 1981. Nevertheless, several versions of the puzzle were created, some of which are still available today. Not all of them are pyramid-shaped, but they are based on the same mechanism and are basically the same. There is also a master pyraminx that has 16 triangles on each side. On the other hand, it is to be distinguished from the Pyramorphix , which looks exactly like a smaller version with four segments per side, but which has a different turning mechanism, which is why, in contrast to the Pyraminx, it changes its shape when released.

Tetraminx

With the Pyraminx, the four corners and middle parts each form a unit, as the corners remain next to the corresponding middle part with every movement. The corners can also be turned, which improves the aesthetics of the puzzle, but does not change the level of difficulty. In fact, there is also a variant of the Pyraminx that has no corner stones and thus resembles a truncated tetrahedron . It is known under the name Tetraminx.

## Combinations and difficulty level

The Pyraminx consists of 14 moving parts of which only ten are relevant, which are significantly fewer than the 20 on the Rubik's Cube. In detail, these are: four corner stones together with the corresponding four middle stones and six edge parts. Since turning individual corners does not change the other parts, the corners are trivial and irrelevant for the solution.

Similar to the normal Rubik's Cube, the central parts of the Pyraminx never change their position to each other, but they can change their orientation, i.e. the three colors change their places. If one ignores the corners, this leads to a theoretical upper limit of 3 4 6! 2 6 positions. Due to the mechanism, however, only a quarter of this can be achieved, resulting in a number of 3 4 6! 2 4 = 933.120 leads. This makes the Pyraminx much simpler than the Rubik's Cube, even than the Pocket Cube , which still has more than 3.6 million positions. The Pyraminx has already been completely calculated algorithmically: Each position requires a maximum of eleven moves to the basic position, not including any turning of the corners. With the inclusion of the four trivial corners, the number of possible positions increases by a factor of 3 4 to 75,582,720.

• Necessary rotations to align the Pyraminx (without rotating the trivial corners)
n 0 1 2 3 4th 5 6th 7th 8th 9 10 11
p 1 8th 48 288 1728 9896 51808 220111 480467 166276 2457 32
• additionally required rotations for the trivial corners
n 0 +1 +2 +3 +4
p 1 8th 24 32 16

The current world record for the fastest one-time release of the Pyraminx is 0.91 seconds and was set by Dominik Górny at the Byczy Cube Race 2018 .

Tymon Kolasiński holds the world record for the average time when solving the Pyraminx five times with 1.86 seconds, set at the Grudziądz Open 2019 .

## mechanics

partially dismantled pyraminx

The mechanics of the Pyraminx are partly similar to that of the 3 × 3 × 3 Rubik's Cube .

There is also an ax cross here. The 4 center stones (one can be seen in the picture at the bottom left) are simply screwed onto this. While the axes of the axles of the classic 3 × 3 × 3 variant are perpendicular to each other, the shape of the axis of this toy is more like a tetrapod . The middle stones are octahedron-shaped , 2 opposite sides have a hole in the middle through which the respective corner piece or the axis cross can be attached. 3 pages can be seen in the assembled state and stuck with stickers and a further 3 pages lie against the edge surfaces.

The corner stones are tetrahedral and are simply placed on the center stones. Each corner stone therefore remains permanently connected to the same, assigned center stone.

The curb stones are also tetrahedral. 2 sides can be seen and pasted, the remaining 2 point inside the Pyraminx. Small plastic parts are attached to the common edge of the 2 surfaces that are not glued. You are always in a recess in a central stone, even when turning. As soon as the edges are turned, these plastic parts continue to run in the recesses inside. So the edges are hooked under the center stones. The indentations are always circular, exactly perpendicular to the opposite tip of the tetrader, so that the sides can be turned as normal as with a Rubik's Cube.

## literature

• Tom Werneck : Magic pyramid. Teufelstonne, Tower, Trikki 4. How to solve the secrets of the new puzzle games . Heyne-Verlag, Munich 1981, ISBN 3-453-41473-X , ( Heyne-Bücher 1, 4833, Heyne-Ratgeber ).