The Square-1 (short for Back to Square One, also known as Cube 21) is a cubic twisty puzzle, with irregular cubies. It's one of the most popular shape-shifting Rubik's Cube variants.
It has only 2 axes of rotation (the top/bottom faces and the entire right/left half of the puzzle).
The puzzle consists of two halves, each with corner and edge pieces indistinguishable to the core. That means that corners can be swapped with edges and otherwise.
The top and bottom layers consist of triangular edge pieces and quadrilateral corner pieces. The middle layer consists of two trapezoidal pieces. When scrambled, it shifts to a random shape : it's a shape-shifting twisty puzzle.
There are 552,738,816,000 positions (170 × 2 × 8! × 8!).
The goal is to return the cube to its cubic state with each side one solid color.
For the silver variation, the goal is only to return the cube to its cubic state.
- Early 1990 : Invention by Dr. Karel Hrsel and Dr. Vojtech Kopsky.
- Early 1990 : Original version is produced by Dr. Karel Hrsel and Dr. Vojtech Kopsky.
- 8 November 1990 : Czechoslovak patent filed on 8 November 1990.
- 26 December 1990 : USA Design patent filed .
- 7 November 1991 : USA Puzzle patent filed .
- 26 October 1992 : Czechoslovak patent approved on 26 October 1992 with patent number 277266 B6.
- 16 March 1993 : USA Puzzle patent approved 16 March 1993 with patent number 5,193,809.
- 5 October 1993 : USA Design patent approved with patent number D340,093.
- 1999 : A version of square-1 with a Cube-21 logo is produced.
- 2003/2004 : WCA is created. Square-1 became an official WCA event.
- 2007 : MF8 also produces the Square-1 since 2007.
- 2010 (or before): CubeTwist also sells a Square-1 produced by YJ since 2010 or before.
- Czechoslovak patent (filed on 8 November 1990 and approved on 26 October 1992 with patent number 277266 B6)
- USA patent :
- Puzzle patent (filed on 7 November 1991 and approved 16 March 1993 with patent number 5,193,809
- Design patent (filed on 26 December 1990 and approved on 5 October 1993 with patent number D340,093)
Original Version (1990)
Original version is produced by Dr. Karel Hrsel and Dr. Vojtech Kopsky during early 1990.
Cube-21 Version (1999)
This is the european version of the cube. The logo was "Cube-21", whiwh is a short for "Cube for 21th century", as it had been produced in 1999. It had also been produced the same year with a "silver edition". In this variation, there are only 2 colors and the goal is simply to shape it back to a cube.
MF8 Version (2007)
MF8 also produces the Square-1 since 2007. It became a more popular cube.
CubeTwist Version (2010 or before)
CubeTwist also sells a Square-1 produced by YJ since 2010 or before.
Square-1 Notation refers to the description of what symbols indicate what moves to apply on a square-1.
The original Square-1 notation, created by Jaap Scherphuis, uses moves of the form (x,y) and moves of the form /. In an (x,y) twist, x indicates the number of 30-degree increments that the top layer should be twisted clockwise (an edge is 30 degrees and a corner is 60 degrees), and y indicates the number of 30-degree increments that the bottom should be twisted clockwise. A / twist simply refers to turning the entire right half of the puzzle by 180 degrees.
It is important to note that in this notation the puzzle must be held so that the layers containing the corners and edges are on the top and bottom, and the middle layer should be in a position so that, on the front side, the shorter middle-layer sticker should be on the left. Thus, from a solved state, the turn (1,-1)/ is possible, but (-1,1)/ is not.
In the newer official notation, adopted by the WCA, there is no /. The WCA regulations (version 2008 v1) say: "(x,y) means: turn upper layer x stickers clockwise, turn bottom layer y stickers clockwise, turn right half of the puzzle 180 degrees. Stickers are counted on the outside of the upper slice." Thus, every (x,y) move is considered to be followed by a / move.
Mike Masonjones proved in 2005 God's Number for the Square-1 to be equal 13 (in the twist metric). That means the puzzle can be solved in 13 twists or less. (12 if the middle layer is ignored).
The puzzle is much easier to work with when it is in the shape of a cube so generally the first step is to somehow (there are several methods) get the pieces arranged so that the puzzle is cubic. Then, the pieces are separated into their correct layers, and permuted. Note that there is no possible incorrect orientation for pieces, since the middle layer can only rotate through 180 degrees at a time (many talks about separation as "orientation").
5-Layers Super Square-1
Greenhill's 5-Layers Square-1
6-Layers Super Square-1
Time Machine II
Wheel of Wisdom
Time Machine : back to Square-1
3 Square in 1
Where to buy
They can be found on Lightake  , on ThatCubeStore  and on many other strores.