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
CONTENTS * 1 Overview * 2 Number of combinations * 3 Optimal solutions * 4 Solving * 5 Variations * 6 See also * 7 References OVERVIEW The
The
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
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: 3 4 4 ! 2 3 = 324 {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
combinations), the
OPTIMAL SOLUTIONS The
As explained above, the total number of possible configurations of
the
N 0 1 2 3 4 TOTAL P 1 8 48 188 79 324 The above table shows that the God\'s Number of the
SOLVING Due to its substantially low number of combinations and its low God's
Number, the
VARIATIONS There are several variations of the
SEE ALSO * Rubik\'s Cube
*
REFERENCES * ^ A B C D Twisty Puzzles - Museum - Rob\'s Pyraminx
* ^ A B Rob\'s
* v * t * e Rubik\'s Cube PUZZLE INVENTORS *
RUBIK\'S CUBES * Overview * 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) CUBIC VARIATIONS *
Non-cubic variations TETRAHEDRON *
OCTAHEDRON *
DODECAHEDRON *
ICOSAHEDRON *
GREAT DODECAHEDRON * Alexander\'s Star TRUNCATED ICOSAHEDRON *
CUBOID *
Virtual variations (>3D) * MagicCube4D * MagicCube5D * MagicCube7D * Magic 120-cell DERIVATIVES * Missing Link * Rubik\'s 360 * Rubik\'s Clock * Rubik\'s Magic * Master Edition * Rubik\'s Revolution * Rubik\'s Snake * Rubik\'s Triamid RENOWNED SOLVERS *
SOLUTIONS SPEEDSOLVING METHODS *
MATHEMATICS * God\'s algorithm
*
OFFICIAL ORGANIZATION RELATED ARTICLES * Rubik\'s Cube in popular culture * The Simple Solution to Rubik\'s Cube * 1982 World Rubik\'s Cube Cha |