The 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. Overview The 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 pieces. 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: This number, in relative terms, is extremely low compared to other puzzles like the