The
Megaminx
Megaminx (/ˈmɛɡəmɪŋks/ or /ˈmeɪ-/) is a
dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total
of 50 movable pieces to rearrange, compared to the 20 movable pieces
of the Rubik's Cube.
Contents
1 History
2 Description
3 Solutions
4 Variations
5 Number of combinations
6 Records
6.1 Top 5 solvers by single solve
6.2 Top 5 solvers by average of 5 solves
7 See also
8 References
9 External links
History[edit]
The Megaminx, or Magic Dodecahedron, was invented by several people
independently and produced by several different manufacturers with
slightly different designs.
Uwe Mèffert eventually bought the rights
to some of the patents and continues to sell it in his puzzle shop
under the
Megaminx
Megaminx moniker.[1] It is also known by the name Hungarian
Supernova, invented by Dr. Cristoph Bandelow.[2] His version came
out first, shortly followed by Meffert's Megaminx. The proportions of
the two puzzles are slightly different.
Description[edit]
The
Megaminx
Megaminx is made in the shape of a dodecahedron, and has 12 faces
and center pieces, 20 corner pieces, and 30 edge pieces. The face
centers each have a single color, which identifies the color of that
face in the solved state. The edge pieces have two colors, and the
corner pieces have three. Each face contains a center piece, 5 corner
pieces and 5 edge pieces. The corner and edge pieces are shared with
adjacent faces. The face centers can only rotate in place, but the
other pieces can be permuted by twisting the face layer around the
face center.
There are two main versions of the Megaminx: one with 6 colors, with
opposite faces having the same color, and one with 12 different
colors. The 12-color
Megaminx
Megaminx is the only type legal in official WCA
competitions, and is therefore much more popular than the 6-color
version.
The purpose of the puzzle is to scramble the colors, and then restore
it to its original state of having one color per face.
Solutions[edit]
The 6-color
Megaminx
Megaminx comes with an additional challenge which is not
immediately obvious (and which does not occur on the 12-color puzzle).
Its edge pieces come in visually identical pairs, because of the
duplicated colors of opposite faces. However, although visually
indistinguishable, they are nevertheless mathematically bound in a
parity relationship. In any legal position (reachable from the solved
state without disassembling the puzzle), there is always an even
number of swapped pairs of edges. However, since swaps may be between
visually identical edges, one may find that having solved almost the
entire puzzle, one is left with a pair of swapped (distinct) edges
that seems to defy all attempts to exchange them. The solution is to
swap a single pair of 'identical' edges to resolve the parity issue,
and then restore the rest of the puzzle.
This property is absent in the 12-color Megaminx, because all its
edges are distinguishable, and it would be immediately obvious that
there is another pair of swapped edges besides the pair one is working
with.
Besides solving a
Megaminx
Megaminx the regular way, patterns can be made on it
just like a Rubik's Cube. Examples of these include a star,
checkerboard, and pentagon in a pentagon patterns.
Variations[edit]
There are many similar puzzles with different numbers of layers, most
of which change the "mega" in the puzzle's name to another metric
prefix. They are the Kilominx (two layers), Master Kilominx (four
layers), Gigaminx (five layers), Elite Kilominx (six layers), Teraminx
(seven layers), Petaminx (nine layers), Examinx (11 layers), Zettaminx
(13 layers), and Yottaminx (15 layers).[3][4] The highest order
mass-produced variant of the
Megaminx
Megaminx is the Petaminx, which was
released by MF8, and the highest order variant of the
Megaminx
Megaminx ever
made to date is the Yottaminx, created by Matt Bahner using 3D
printing. It is the dodecahedral equivalent to a 15×15×15 Rubik's
cube.
Alexander's Star
Alexander's Star is equivalent to solving only the edges of a
six-color Megaminx.
The
Impossiball
Impossiball is equivalent to solving only the corners of a
Megaminx
Megaminx and is available with either six or twelve colors.
The
Pyraminx Crystal
Pyraminx Crystal is a modified
Megaminx
Megaminx with deeper turning
planes.
Tony Fisher has produced a shape modification of the
Megaminx
Megaminx into a
cube form which he called the Hexaminx.[5] Another variant is the
Holey Megaminx, which has no center pieces, like the Void Cube. It is
being produced by Mèffert as of July 2009. Other variants include the
Flowerminx,
Megaminx
Megaminx Ball, and Crazy Megaminx.
A Holey Megaminx, with black body
Kilominx, Megaminx, Master Kilominx, Gigaminx, Elite Kilominx,
Teraminx
Number of combinations[edit]
Play media
Ernesto González solving a
Megaminx
Megaminx at TLP Tenerife 2017
Both versions of the
Megaminx
Megaminx have 20 corners and 30 edges. In both
cases, only even permutations are possible, regardless of the position
of the other set of pieces. Thus, while it is possible to have a
single pair of corners and a single pair of edges swapped on a Rubik's
Cube, this is impossible on the Megaminx. There are 20!/2 ways to
arrange the corners and 319 ways to orient them, since the orientation
of the last corner depends on that of the preceding ones. There are
30!/2 ways to arrange the edges and 229 ways to flip them.
20
!
×
3
19
×
30
!
×
2
27
≈
1.01
×
10
68
displaystyle 20!times 3^ 19 times 30!times 2^ 27 approx 1.01times
10^ 68
The full number is 100 669 616 553 523 347 122 516 032 313 645 505
168 688 116 411 019 768 627 200 000 000 000 (roughly 101
unvigintillion on the short scale or 101 undecillion on the long
scale).
The corners are distinguishable on a 6-color
Megaminx
Megaminx because two
corners with the same three colors will be mirror images of each
other. There are 15 pairs of identical edges. It would not be possible
to swap all 15 pairs, since this would be an odd permutation of the
edges, so a reducing factor of 214 is applied to the preceding figure.
20
!
×
3
19
×
30
!
×
2
13
≈
6.14
×
10
63
displaystyle 20!times 3^ 19 times 30!times 2^ 13 approx 6.14times
10^ 63
The full number is 6 144 385 775 971 883 979 645 753 925 393 402 415
081 061 792 664 780 800 000 000 000 (roughly 6.1 vigintillion on the
short scale or 6.1 decilliard on the long scale).
For the larger size variations (gigaminx, teraminx, petaminx etc), the
general number of combinations is
30
!
×
20
!
×
60
!
n
2
−
1
×
2
28
−
n
×
3
19
5
!
12
n
(
n
−
1
)
displaystyle frac 30!times 20!times 60!^ n^ 2 -1 times 2^ 28-n
times 3^ 19 5!^ 12n(n-1)
where
n
=
1
,
2
,
3
,
4
,
.
.
.
displaystyle n=1,2,3,4,...
respectively for megaminx, gigaminx, teraminx, petaminx, etc.[6] The
number of combinations evaluates to
3.65
×
10
263
displaystyle 3.65times 10^ 263
for gigaminx,
1.15
×
10
573
displaystyle 1.15times 10^ 573
for teraminx, and
3.16
×
10
996
displaystyle 3.16times 10^ 996
for petaminx.
Records[edit]
Speedsolvers completing Megaminxes at the Estonian Open 2011.
The world record time for a
Megaminx
Megaminx solve is 29.93 seconds, set by
Juan Pablo Huanqui of Peru on 11 June 2017 at LatAm Tour - Santiago
2017. [7] Huanqui also holds the record for average of five solves
(excluding best and worst), 35.15 seconds, also set on 11 June 2017 at
LatAm Tour - Santiago 2017. Huanqui has 18 of the fastest 19
averages.[8]
Top 5 solvers by single solve[edit]
Name
Fastest solve
Competition
Juan Pablo Huanqui
29.93s
LatAm Tour - Santiago 2017
Yu Da-Hyun (유다현)
30.12s
CWR Winter 2018
Feliks Zemdegs
34.60s
LatAm Tour - Guatemala 2017
Nicolas Naing
35.94s
Big Apple Spring 2016
Henri Gerber
36.24s
Hessen Open 2017
Top 5 solvers by average of 5 solves[edit]
Name
Fastest average
Competition
Yu Da-Hyun (유다현)
32.03s
CWR Winter 2018
Juan Pablo Huanqui
35.15s
LatAm Tour - Santiago 2017
Feliks Zemdegs
41.63s
Canberra Spring 2017
Andy Denney
42.66s
Grind City 2018
Nicolas Naing
43.07s
Big Apple Spring 2016
See also[edit]
Impossiball
Alexander's Star
Pyraminx
Pyraminx Crystal
Rubik's Cube
Pyraminx
Skewb
Skewb Diamond
Tuttminx
Dogic
Combination puzzles
Magic 120-cell
References[edit]
^ Jaap's puzzle page, Megaminx
^ twistypuzzles.com, Hungarian Supernova
^ Gigaminx and Teraminx Archived 2009-06-06 at the Wayback Machine.
(in Italian)
^ Video of Petaminx
^ Slocum, Jerry (2009), The Cube: The Ultimate Guide to the World’s
Best Selling Puzzles. Black Dog & Leventhal Publishers.
ISBN 978-1-57912-805-0.
^ Generalized number of permutations for all twisty puzzles. Search
the page for Megaminx.
^ https://www.worldcubeassociation.org/results/regions.php
^
https://www.worldcubeassociation.org/results/events.php?eventId=minx®ionId=&years=&show=100%2BPersons&average=Average
External links[edit]
Meffert's puzzle shop
Jaap's
Megaminx
Megaminx page—contains solutions and other information
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)
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
Helicopter Cube
Skewb
Square 1
Sudoku Cube
Nine-Colour Cube
Void Cube
Non-cubic
variations
Tetrahedron
Pyraminx
Pyraminx
Pyraminx Duo
Pyramorphix
BrainTwist
Octahedron
Skewb
Skewb Diamond
Dodecahedron
Megaminx
Megaminx (Variations)
Pyraminx
Pyraminx Crystal
Skewb
Skewb Ultimate
Icosahedron
Impossiball
Dogic
Great dodecahedron
Alexander's Star
Truncated icosahedron
Tuttminx
Cuboid
Floppy Cube
Floppy Cube (1x3x3)
Rubik's Domino
Rubik's Domino (2x3x3)
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
Rubik's Cheese
Renowned solvers
Erik Akkersdijk
Yu Nakajima
Bob Burton, Jr.
Jessica Fridrich
Chris Hardwick
Rowe Hessler
Leyan Lo
Shotaro Makisumi
Toby Mao
Tyson Mao
Frank Morris
Lars Petrus
Gilles Roux
David Singmaster
Ron van Bruchem
Eric Limeback
Anthony Michael Brooks
Mats Valk
Feliks Zemdegs
Collin Burns
Lucas Etter
Solutions
Speedsolving
Speedcubing
Methods
Layer by Layer
CFOP Method
Roux Method
Corners First
Optimal
Mathematics
God's algorithm
Superflip
Thistlethwaite's algorithm
Rubik's Cube
Rubik's Cube group
Official organization
World Cube Association
Related articles
Rubik's Cube
Rubik's Cube in popular culture
The Simple Solution to Rubik's Cube
1982 World Rubik's