The
Pyramorphix
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 Pyraminx, it is an
edge-turning puzzle with the mechanism identical to that of the Pocket
Cube.
Contents
1 Description
2 Number of combinations
3 Master Pyramorphix
3.1 Solutions
3.2 Number of combinations
4 See also
5 References
6 External links
Description[edit]
At first glance, the
Pyramorphix
Pyramorphix appears to be a trivial puzzle. It
resembles the Pyraminx, and its appearance would suggest that only the
four corners could be rotated. In fact, the puzzle is a specially
shaped 2×2×2 cube, if the tetrahedron is considered to be demicube.
Four of the cube's corners are reshaped into pyramids and the other
four are reshaped into triangles. The result of this is a puzzle that
changes shape as it is turned.
The original name for the
Pyramorphix
Pyramorphix was "The Junior Pyraminx." This
was altered to reflect the "Shape Changing" aspect of the puzzle which
makes it appear less like the 2x2x2 Rubik Cube. "Junior" also made it
sound less desirable to an adult customer. The only remaining
reference to the name "Junior Pyraminx" is on Uwe Mèffert's
website-based solution which still has the title "jpmsol.html".[1][2]
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[edit]
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
Pyramorphix
Pyramorphix can be rotated around three axes by multiples of 90°.
The corners cannot rotate individually as on the Pyraminx. The
Pyramorphix
Pyramorphix rotates in a way that changes the position of center
pieces not only with other center pieces but also with corner pieces,
leading to a variety of shapes.
Master Pyramorphix[edit]
The Master Pyramorphix
The Master Pyramorphix, color-scrambled
The Master Pyramorphix, color- and shape- scrambled
The Master Pyramorphix, partially solved
The Master Pyramorphix, with maximal face-piece flip, equivalent to
the "superflip" configuration of the 3x3x3 Rubik's Cube
The Master
Pyramorphix
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 Uwe Mèffert's commercially produced
pillowed variant (pictured), sold through his puzzle shop, Meffert's.
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
Pyraminx
Pyraminx is that they are both "twisty puzzles"; the
Pyraminx
Pyraminx is a face-turning puzzle. On the Mastermorphix the corner
pieces are non-trivial; they cannot be simply rotated in place to the
right orientation.
Solutions[edit]
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
Rubik's Cube
Rubik's Cube with a non-standard coloring
scheme where center piece orientation matters, and the orientation of
4 of the 8 corner pieces do not, technically, matter.
Unlike the Square One, another shape-changing puzzle, the most
straightforward solutions of the Master
Pyramorphix
Pyramorphix do not involve
first restoring the tetrahedral shape of the puzzle and then restoring
the colors; most of the algorithms carried over from the 3x3x3 Rubik's
Cube translate to shape-changing permutations of the Master
Pyramorphix. Some methods, such as the equivalent of Philip Marshall's
"Ultimate Solution", show a gradual progression in shape as the
solution progresses; first the non-center face pieces are put into
place, resulting in a partial restoration of the tetrahedral shape
except at the face centers and corners, and then the complete
restoration of tetrahedral shape as the face centers and corners are
solved.
Number of combinations[edit]
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 7022885801027061552♠88580102706155225088000.
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 7018506287738375372♠5062877383753728000.
See also[edit]
Skewb
Skewb Diamond
Skewb
Skewb Ultimate
Combination puzzles
Mechanical puzzles
References[edit]
^ http://www.mefferts.com/puzzles/jpmsol.html
^ http://www.angelfire.com/trek/andysuth/d.html
External links[edit]
Jaap's
Pyramorphix
Pyramorphix page
A Java applet which includes the Pyramorphix
Speedsolving.com Wiki - Solution (Master Pyramorphix)
v
t
e
Rubik's Cube
Puzzle inventors
Ernő Rubik
Uwe Mèffert
Tony Fisher
Panagiotis Verdes
Oskar van Deventer
Rubik's Cubes
Overview
2×2×2 (Pocket Cube)
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Related articles
Rubik's Cube
Rubik's Cube in popular culture
The Simple Solution to Rubik's Cube
1982 World
Rubik's Cube
Rubik's Cube