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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&regionId=&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

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