## The 2x2 Rubik's Cube Octahedron Series

One of the playgrounds in Trinagon is the dual body to the cube, the octahedron.
The octahedron has as many vertices (corners) as the cube has faces, and vice versa.

If you visualise the triangles being the cornerstones of a cube you will see a 2x2 rubik's cube.

A mathematically completely identical puzzle to the Rubik's cube can be seen above.
The only difference is the absolute position of the triangles, whereas the corners of the 2x2 rubik's cube are solved relative to each other.

In honor of the Rubik's Cube, we made a few puzzles using 8 colors, which correspond to the 8 corners of the cube, and therefore resemble the 2x2 cube the most, and named this collection after that fact.
Shuffle those to play them rubik's-cube-style.

Trinagon also offers easier variations and a few symetrical patterns that have secifically been made to resemble the typical problems coming up when solving a rubik's 2x2 cube.
That is why they almost look repetitive, but aren't. Each offers a different 2x2 cube-dual-problem to solve.
You might even learn some new tricks on these, and find more elegant ways to solve the cube.

Here they are. From easy to hardest. More of them may be made.

A simple color exchange. The triangles are exactly opposite their solved positions.
With no faces or direction markers on, this puzzle can be solved rather easily.
Puzzle Nr. 152532
Difficulty : 20
Rotator Type 1

Best solution : To be seen... by  AnonyMouse, 23.11.2019

The same as the previous puzzle but at the same time the faces have to be switched.

Puzzle Nr 183953
Rotator Type 4

You shall find out how much more difficult this one is compared to the last. Maybe not by much ?

Best solution : ....

Here the pieces end up at the same spot, but with their faces switched.
Only the solution (in the corner) is different.

This puzzle is less obviously like the rubik's cube, because the cube would only use rotation type 1.
Also for an extra challenge two rotators are missing !

Puzzle Nr. 465970
Difficulty : ??
Rotator Type 1 & 4

Best solution : ....

The third step on the same theme, with face and directions active !
The triangles sit exactly opposite their intended location. They are directed 'up and down' to the black rotators.
Maybe a similar pattern to solving it exists as in puzzles 152532 & 183953 ?

Puzzle Nr. 379894
Difficulty : ??
Rotator Type 4

Best solution : ....

Now it gets a bit harder. Here the red, green, purple & grey triangles are already there, but yellow <-> orange & blue <-> pink need to be exchanged.

This is one case where a color-only puzzle is not easy anymore. The cube-duality is the reason for that.

Puzzle Nr. 623675
Difficulty : 40
Rotator Type 1

Best solution : ....

Mathematically identical to the rubik's cube, with only rotation 1 in use, and directionmarkers active.
The symytry is the same as puzzle 379894, i.e. the triangles simply opposite their intented spot.

We're not sure if this one is harder or easier than the last. The specific symetry may make it easier ? (we know, but won't say :))

Puzzle Nr. 048838
Difficulty : ??
Rotator Type 1

Best solution : ....

If you want to play 2x2 rubik's cube style, shuffle this one. It sould be possible to solve in 14 moves, at least by a god, or maybe by you.

### These next three puzzles have not been solved yet :

Same as puzzle 623675, but facemarkers active and playing with mixed rotations.
This puzzle would impossible, if not for the face-preserving rotationtype in it.

As it is, it has not yet been solved !!!  but theory alone claims that it is solvable !
Feel free to send in your solutions !

Puzzle Nr. 616545
Difficulty : actually unknown, since it has not been solved, but designed from theory.
This one is likely harder than the two below.
Rotator Types 2, 4 & 6

Best solution : tba

Same as puzzle 048838 but with the color-symetry of 623675, i.e. four colors have been switched.

Also unsolved. Theory says it is, and we'll be happy to put your name under it.

Puzzle Nr. 605522
Difficulty : as hard as a shuffled 2x2 rubik's cube with absolute positions.
Rotator Type 1

Best solution : tba

Another Variation on switching colors. This one switches 4 colors vertical (vertical = between the black rotators, one defined as 'up' the other as 'down') and the other 4 colors horizontally.

Puzzle Nr. 564784
Difficulty : most likely harder than the one before ?
Rotator Type 1

Also unsolved. Theory says it is, and we'll be happy to put your name under it.

Best solution : tba.

With these three not being played (&solved) yet, please send your solution to lumpazy. The best solution shall be remembered right here.

Some of the others have only been played once, so there is room to earn some genius points.
How many moves the best solution really needs is unclear. With the symetries in play they mostly should be solvable in less than 14 moves. When some of the rotators have been left out or when playing mixed rotations, this number may be going up a bit - or not !
You are invited to help find the best solutions :)