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
Tomy Toys of Japan (then the 3rd largest toy company in
the world) in 1981.
2 Optimal solutions
6 See also
8 External links
Pyraminx in the middle of a twist
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
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
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
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:
Solving a pyraminx in competition. Andreas Pung at Estonian Open 2011.
The world record fastest
Pyraminx solve is 1.20 seconds, set by Tymon
Poland on 13 January 2018 at Speed Days Kraśnik 2018.
The world record fastest average of five
Pyraminx solves (excluding
fastest and slowest) is 2.02 seconds, set too by Tymon Kolasiński of
Poland on 9 December 2017 at the GLS Final 2017.
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 three edges around a corner are
solved first, and the remaining is solved using a set of algorithms.
Common V first methods-
Layer by Layer - In this method a face with all edges oriented in
the right spot (a.k.a. a layer) is solved and then the remaining
puzzle is solved by a single algorithm from a set of 5.
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 a lot of visualization is required. The set of algorithms
mentioned in the previous method are not memorized. In speedsolving,
cases are solved intuitively 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
center, 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 (a.k.a. keyhole).
The last step is solved using Keyhole last layer algorithms.
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 algorithms.
Some other common top first methods are WO and Nutella.
Pyraminx speedsolvers learn several methods, and while observing
a case, decide which method best suits that case.
A solved Tetraminx.
There are several variations of the puzzle. The simplest, Tetraminx,
is equivalent to the (3x)
Pyraminx but without the tips (see photo).
There also exist "higher-order" versions, such as the 4x Master
Pyraminx (see photos) and the 5x Professor's Pyraminx.
A basic pattern on a Master Pyraminx
A solved Master Pyraminx
Pyraminx has 4 layers and 16 triangles-per-face (compared
to 3 layers and 9 triangles-per-face of the original). This version
has about 2.17225 × 1017 combinations. The Master
4 "tips" (same as the original Pyraminx)
4 "middle axials" (same as the original Pyraminx)
4 "centers" (similar to Rubik's Cube, none in the original Pyraminx)
6 "inner edges" (similar to Rubik's Cube, none in the original
12 "outer edges" (2-times more than the 6 of the original Pyraminx)
In summary, the Master
Pyraminx has 30 "manipulable" pieces. However,
like the original, 8 of the pieces (the tips and middle axials) are
fixed in position (relative to each other) and can only be rotated in
place. Also, the 4 centers are fixed in position and can only rotate
(like the Rubik's Cube). So there are only 18 (30-8-4) "truly movable"
pieces; since this is 10% less than the 20 "truly movable" pieces of
the Rubik's Cube, it should be no surprise that the Master Pyraminx
has about 200-times fewer combinations than a
Rubik's Cube (about
4.3252 × 1019).
Pyramorphix and Master Pyramorphix, two regular tetrahedron puzzles
which resemble the
Pyraminx but are mechanically very different from
Pyraminx - Jaap's Puzzle Page
Pyraminx - Official World Records (Single and Average)". World Cube
Association. Retrieved 4 August 2016.
World Cube Association - Drew Brads results.
^ "Full List of Puzzles". gandreas software. Retrieved
^ "Notes on Twisty Puzzles". Michael Gottlieb. Retrieved
^ Martin Schönert "Analyzing
Rubik's Cube with GAP": the permutation
Rubik's Cube is examined with GAP computer algebra system
Wikimedia Commons has media related to Pyraminx.
Pyraminx and related puzzles page, with solution
Pyraminx solution from PuzzleSolver
A solution to the Pyraminx[permanent dead link] by Jonathan Bowen
An efficient and easy to follow solution favoured by speed solvers
Patterns A collection of pretty patterns for the Pyraminx
Oskar van Deventer
2×2×2 (Pocket Cube)
3×3×3 (Rubik's Cube)
4×4×4 (Rubik's Revenge)
5×5×5 (Professor's Cube)
6×6×6 (V-Cube 6)
7×7×7 (V-Cube 7)
8×8×8 (V-Cube 8)
Floppy Cube (1x3x3)
Rubik's Domino (2x3x3)
Bob Burton, Jr.
Ron van Bruchem
Anthony Michael Brooks
Layer by Layer
Rubik's Cube group
World Cube Association
Rubik's Cube in popular culture
The Simple Solution to Rubik's Cube
1982 World Rubik's