Pyraminx Duo (originally known as Rob's Pyraminx) is a
tetrahedral twisty puzzle in the style of the Rubik's Cube. It was
suggested by Rob Stegmann, invented by Oskar van Deventer,
and has now been mass-produced by Meffert's.
2 Number of combinations
3 Optimal solutions
6 See also
Pyraminx Duo in the middle of a twist, showing how the puzzle can
Pyraminx Duo is a puzzle in the shape of a tetrahedron, divided
into 4 corner pieces and 4 face centre pieces. Each corner piece has
three colours, while the centre pieces each have a single colour. Each
face of the puzzle contains one face centre piece and three corner
The puzzle can be thought of as twisting around its corner pieces -
each twist rotates one corner piece and permutates the three face
centre pieces around it. An interesting feature is that the face
centre pieces go "underneath" corner pieces during a twist.
The purpose of the puzzle is to scramble the colours, and then restore
them to their original configuration of one colour per face.
Mechanically, the puzzle is similar to the Skewb, with all corner
pieces of the
Skewb visible (although shaped differently) and all
centre pieces hidden.
Number of combinations
There are 4 corner pieces. Each corner can be twisted in 3 different
orientations, independently of the other corners. Therefore, the
corners can be orientated in 34 different ways. They cannot be
permutated, therefore there is only one possible corner permutation.
There are 4 face centre pieces. These can be permutated in at most 4!
different ways. However, the exact number of these permutations is not
yet reached due to two constraints. The first constraint is that only
even permutations of the face centers are possible (e.g. it is
impossible to have only two face centre pieces swapped); this divides
the limit by 2. The second constraint is that all centre permutations
are dependent on the orientation of the corner pieces. Some
permutations of centres are only possible when the total number of
clockwise rotations of corner pieces is divisible by 3; other
permutations are only possible when the total number of clockwise
rotations is equivalent to 1 modulo 3; others are only possible when
the number is equivalent to 2 modulo 3. This divides the limit by 3.
The face centre pieces have no obvious orientation, therefore this
does not affect the total number of combinations.
The full number is therefore:
displaystyle frac 3^ 4 times 4! 2times 3 =324
This number, in relative terms, is extremely low compared to other
puzzles like the
Rubik's Cube (which has over 43 quintillion
Pocket Cube (with over 3.6 million combinations),
or even the
Pyraminx (with just over 930 thousand combinations,
excluding rotations of the trivial tips).
Pyraminx Duo, scrambled.
As explained above, the total number of possible configurations of the
Pyraminx Duo is 324, which is sufficiently small to allow a computer
search for optimal solutions. The table below summarises the result of
such a search, stating the number p of positions that require n twists
to solve the
The above table shows that the God's Number of the
Pyraminx Duo is 4
(i.e. the puzzle is always at most 4 twists away from its solved
state). Similarly to the total number of combinations, this number is
very low compared to the
Rubik's Cube (20), the
Pocket Cube (11) or
Pyraminx (11, excluding the trivial tips).
Due to its substantially low number of combinations and its low God's
Pyraminx Duo is a relatively easy puzzle to solve; it has
been described as "arguably the easiest non-trivial twisty puzzle".
Because of this, cubers usually come up with their own methods of
solving the puzzle. For an extra challenge, it is also not uncommon
for cubers to invent their own "optimal" methods - i.e. methods that
guarantee to solve the puzzle in no more than 4 moves.
There are several variations of the
Pyraminx Duo that have been
invented. These variations all look the same as the original puzzle
but use different colour schemes; usually these colour schemes make
the orientations of the face centre pieces visible, which makes the
puzzle slightly more challenging.
^ a b c d Twisty Puzzles - Museum - Rob's Pyraminx
^ a b Rob's
Pyraminx - YouTube
Pyraminx Duo Black - Meffert's
^ a b c
Pyraminx Duo - Jaap's Puzzle Page
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