![Tuttminx01](https://upload.wikimedia.org/wikipedia/commons/f/ff/Tuttminx01.jpg)
A Tuttminx ( or ) is a
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
-like twisty puzzle, in the shape of a
truncated icosahedron
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It is the only one of these shapes that does not contain triangles or squares. ...
. It was invented by Lee Tutt in 2005. It has a total of 150 movable pieces to rearrange, compared to 20 movable pieces of the Rubik’s Cube.
Description
The Tuttminx has a total of 32 face centre pieces (12 pentagon and 20 hexagon), 60 corner pieces, and 90 edge pieces. The face centres each have a single colour, which identifies the colour of that face in the solved state. The edge pieces have two colours, and the corner pieces have three colours. Each hexagonal face contains a centre piece, 6 corner pieces, and 6 edge pieces, while each pentagonal face contains a centre piece, 5 corner pieces, and 5 edge pieces.
The puzzle twists around the faces: each twist rotates one face centre piece and moves all edge and corner pieces surrounding it. The pentagonal faces can be twisted 72° in either direction, while the hexagonal faces can be rotated 120°.
The purpose of the puzzle is to scramble the colours, and then restore it to its original state of having one colour per face.
Number of combinations
The puzzle has 150 movable pieces: 60 corner pieces, 60 edge pieces that are adjacent to a pentagonal face (so-called pentagonal edges) and 30 edge pieces that are not (non-pentagonal edges). Only even permutations of all three types of pieces are possible (i.e. it is impossible to have only one pair of identical pieces swapped). Thus, there are 60!/2 possible ways to arrange the corner pieces, 60!/2 ways to arrange the pentagonal edges and 30!/2 ways to arrange the non-pentagonal edges.
All corner pieces have only one possible orientation, as do all pentagonal edge pieces. The non-pentagonal edge pieces all have 2 possible orientations each. Only even orientations of those are possible (meaning that it is impossible to have only one edge piece flipped over). This means there are 2
29 ways to orientate the edge pieces.
The number of possible combinations on the Tuttminx is therefore equal to
:
The full number is 1 232 507 756 161 568 013 733 174 639 895 750 813 761 087 074 840 896 182 396 140 424 396 146 760 158 229 902 239 889 099 665 575 990 049 299 860 175 851 176 152 712 039 950 335 697 389 221 704 074 672 278 055 758 253 470 515 200 000 000 000 000 000 000 000 000 000 000 000 (about 1.2325 septensexagintillion on the
short scale
The long and short scales are two of several naming systems for integer power of 10, powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one m ...
and 1.2325 quattuortrigintillion on the long scale).
Variations
There are a few variations of the Tuttminx that have been made. The most popular ones include:
* Void Tuttminx, which is a regular Tuttminx but without the face centre pieces;
* Rayminx (, also called ''Giga Tuttminx''), which is a higher-order version of the Tuttminx;
* Futtminx, which was invented by
Oskar van Deventer
Oskar van Deventer (born 1965) is a Dutch puzzle maker. He prototypes puzzles using 3D printing. His work combines mathematics, physics, and design, and he collaborates at academic institutions. Many of his combination puzzles are in mass produc ...
and has been designed so that the hexagonal faces can be rotated 60° and mix up with the pentagonal faces.
* Love bird, a 2x2x2 version of the Tuttminx.
* Tuttminx ball, also sticker variations of that.
* Chamfered dodecahedron tuttminx. It looks similar to the Tuttminx, but hexagons are located differently, they are distorted, and there are more of them (30 instead of 20).
See also
*
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
*
Megaminx
The Megaminx or Mégaminx (, ) 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.
History
The Megaminx, or Magic Dodecahedron, ...
*
Helicopter Cube
The Helicopter Cube is a Rubik's Cube-like puzzle invented by Adam G. Cowan in 2005 and built in 2006. It is also in the shape of a cube. At first glance, the Helicopter Cube may seem like a combination of the 2x2x2 and the Skewb, but it actually ...
*
Pyraminx Crystal
The Pyraminx Crystal (also called a Chrysanthemum puzzle) is a dodecahedral puzzle similar to the Rubik's Cube and the Megaminx. It is manufactured by Uwe Mèffert and has been sold in his puzzle shop since 2008.
The puzzle was originally call ...
*
Goldberg Polyhedron
In mathematics, and more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described in 1937 by Michael Goldberg (1902–1990). They are defined by three pro ...
References
{{Rubik's Cube
Combination puzzles
Mechanical puzzles