Square1 (puzzle type)

The Square1 (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 shapeshifting Rubik's Cube variants.
Contents
Description
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 shapeshifting twisty puzzle. There are 552,738,816,000 positions (170 × 2 × 8! × 8!).
Goal
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.
History
 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 square1 with a Cube21 logo is produced.
 2003/2004 : WCA is created. Square1 became an official WCA event.
 2007 : MF8 also produces the Square1 since 2007.
 2010 (or before): CubeTwist also sells a Square1 produced by YJ since 2010 or before.
Patents
 Czechoslovak patent (filed on 8 November 1990 and approved on 26 October 1992 with patent number 277266 B6)
 USA patent :
Producers
Original Version (1990)
Original version is produced by Dr. Karel Hrsel and Dr. Vojtech Kopsky during early 1990.
Cube21 Version (1999)
This is the european version of the cube. The logo was "Cube21", 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 Square1 since 2007. It became a more popular cube.
CubeTwist Version (2010 or before)
CubeTwist also sells a Square1 produced by YJ since 2010 or before.
Square1 Notation
Main Article : Square1 notation 
Square1 Notation refers to the description of what symbols indicate what moves to apply on a square1.
The original Square1 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 30degree 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 30degree 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 middlelayer 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 Square1 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).
Methods
Main Article : Square1 methods 
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").
Variations
Super Square1
Main Article : Super Square1 (puzzle type) 
Invented at the same time by James Lee and an unidentified person in 2007, the Super Square1 is a Square1 with 4 layers. It's massproduced since 2008 by MF8.
Square2
Main Article : Square2 (puzzle type) 
Firstly built by David Litwin in 1995, the Square2 is an unbandaged version of Square1 : corners are cut in half. Then, it has been independently built by Jake and Noda in 2003, and by many people in 2008. The name Square2 has been choosen by Noda. It's massproduced since 2012 by hknowstore.
2Layers Square1
Main Article : 2Layers Square1 (puzzle type) 
Firstly built by Li Chung Man in 2008, the 2Layers Square1 is a version of Square1 with 2 layers. It can be easily built out of a Super Square1. It's massproduced by QJ.
Square1II
Main Article : Square1II (puzzle type) 
Firstly built by Anthony Greenhill in 2002, the Square1II is a version of Square1 with 2 layers : the middle layer has been removed.
Ghost Square1
Main Article : Ghost Square1 (puzzle type) 
Ghost Square1 is a shapetransfomation of Square1. There are different versions : Rex Rossano Perez in 2016, Aj Lu in 2013, ...
5Layers Super Square1
Main Article : 5Layers Super Square1 (puzzle type) 
Claus Wenicker built a version of Super Square1 with 5 layers in 2010.
Greenhill's 5Layers Square1
Main Article : Greenhill's 5Layers Square1 (puzzle type) 
Anthony Greenhill built a version of Square1 with 5 layers in 2003.
6Layers Super Square1
Main Article : 6Layers Super Square1 (puzzle type) 
Claus Wenicker built the 5Layers Super Square1 with a 6Layers Super Square1, that has been invented in 2010.
Time Machine
Main Article : Time Machine (puzzle type) 
Firstly built by Li Chung Man in 2009, the Time Machine is a mix between a 2x2x2 and 3 Square2. Its first name was Pipe Connector.
Time Machine II
Main Article : Time Machine II (puzzle type) 
A J Lu made a Time Machine II in 2010. It is a mix between a 1x2x2 and 3 Square2.
Wheel of Wisdom
Main Article : Wheel of Wisdom (puzzle type) 
Massproduced by Dayan and invented by Daqing Bao in 2013
Time Machine : back to Square1 / 3 Square in 1
Main Article : Time Machine : back to Square1 (puzzle type) 
Main Article : 3 Square in 1 (puzzle type) 
Invented by Li Chung Man in 2011 and Olivier Polspoel in 2008, this is a mix between a 2x2x2 and 3 Square1. It's a bandaged version of Time Machine. The difference between these 2 puzzles is only the shape.
Square1 Software
See also
External links
