The PYRAMORPHIX (/ˌpɪrəˈmɔːrfɪks/ , often misspelt
Pyramorphinx) is a tetrahedral puzzle similar to the Rubik\'s Cube .
It has a total of 8 movable pieces to rearrange, compared to the 20 of
the Rubik's Cube. Though it looks like a simpler version of the
CONTENTS * 1 Description * 2 Number of combinations * 3 Master
* 3.1 Solutions * 3.2 Number of combinations * 4 See also * 5 References * 6 External links DESCRIPTION At first glance, the
The original name for the
The purpose of the puzzle is to scramble the colors and the shape, and then restore it to its original state of being a tetrahedron with one color per face. NUMBER OF COMBINATIONS The puzzle is available either with stickers or plastic tiles on the faces. Both have a ribbed appearance, giving a visible orientation to the flat pieces. This results in 3,674,160 combinations, the same as the 2×2×2 cube. However, if there were no means of identifying the orientation of those pieces, the number of combinations would be reduced. There would be 8! ways to arrange the pieces, divided by 24 to account for the lack of center pieces, and there would be 34 ways to rotate the four pyramidal pieces. 8 ! 3 4 24 = 136080 {displaystyle {frac {8!times 3^{4}}{24}}=136080} The
MASTER PYRAMORPHIX The Master
The MASTER PYRAMORPHIX is a more complex variant of the Pyramorphix.
Although it is officially called the Master Pyramorphix, most people
refer to it as the "Mastermorphix". Like the Pyramorphix, it is an
edge-turning tetrahedral puzzle capable of changing shape as it is
twisted, leading to a large variety of irregular shapes. Several
different variants have been made, including flat-faced custom-built
puzzles by puzzle fans and
The puzzle consists of 4 corner pieces, 4 face centers, 6 edge pieces, and 12 non-center face pieces. Being an edge-turning puzzle, the edge pieces only rotate in place, while the rest of the pieces can be permuted. The face centers and corner pieces are interchangeable because they are both corners although they are shaped differently, and the non-center face pieces may be flipped, leading to a wide variety of exotic shapes as the puzzle is twisted. If only 180° turns are made, it is possible to scramble only the colors while retaining the puzzle's tetrahedral shape. When 90° and 180° turns are made this puzzle can "shape shift″. In spite of superficial similarities, the only way that this puzzle
is related to the
SOLUTIONS Despite its appearance, the puzzle is in fact equivalent to a shape
modification of the original 3x3x3 Rubik's Cube. Its 4 corner pieces
on the corners and 4 corner pieces on the face centers together are
equivalent to the 8 corner pieces of the Rubik's Cube, its 6 edge
pieces are equivalent to the face centers of the Rubik's Cube, and its
non-center face pieces are equivalent to the edge pieces of the
Rubik's Cube. Thus, the same methods used to solve the Rubik's Cube
may be used to solve the Master Pyramorphix, with a few minor
differences: the center pieces are sensitive to orientation because
they have two colors, unlike the usual coloring scheme used for the
Rubik's Cube, and the face centers are not sensitive to orientation
(however when in the "wrong" orientation parity errors may occur). In
effect, it behaves as a
Unlike the Square One , another shape-changing puzzle, the most
straightforward solutions of the Master
NUMBER OF COMBINATIONS There are four corners and four face centers. These may be interchanged with each other in 8! different ways. There are 37 ways for these pieces to be oriented, since the orientation of the last piece depends on the preceding seven, and the texture of the stickers makes the face center orientation visible. There are twelve non-central face pieces. These can be flipped in 211 ways and there are 12!/2 ways to arrange them. The three pieces of a given color are distinguishable due to the texture of the stickers. There are six edge pieces which are fixed in position relative to one another, each of which has four possible orientations. If the puzzle is solved apart from these pieces, the number of edge twists will always be even, making 46/2 possibilities for these pieces. 8 ! 3 7 12 ! 2 9 4 6 8.86 10 22 {displaystyle {8!times 3^{7}times 12!times 2^{9}times 4^{6}}approx 8.86times 10^{22}} The full number is 88 580 102 706 155 225 088 000. However, if the stickers were smooth the number of combinations would be reduced. There would be 34 ways for the corners to be oriented, but the face centers would not have visible orientations. The three non-central face pieces of a given color would be indistinguishable. Since there are six ways to arrange the three pieces of the same color and there are four colors, there would be 211×12!/64 possibilities for these pieces. 8 ! 3 4 12 ! 2 10 4 6 6 4 5.06 10 18 {displaystyle {frac {8!times 3^{4}times 12!times 2^{10}times 4^{6}}{6^{4}}}approx 5.06times 10^{18}} The full number is 5 062 877 383 753 728 000. SEE ALSO *
REFERENCES * ^ http://www.mefferts.com/puzzles/jpmsol.html * ^ http://www.angelfire.com/trek/andysuth/d.html EXTERNAL LINKS * |