Editing Tetromino (section)

==Types of tetrominoes==
===Free tetrominoes===
Polyominos are formed by joining unit squares along their edges. A [[free polyomino]] is a polyomino considered up to [[congruence (geometry)|congruence]]. That is, two free polyominos are the same if there is a combination of [[translation (geometry)|translation]]s, [[rotation (mathematics)|rotation]]s, and [[reflection (mathematics)|reflection]]s that turns one into the other. A free tetromino is a free polyomino made from four squares. There are five free tetrominoes.

The free tetrominoes have the following symmetry:
* Straight: vertical and horizontal reflection symmetry, and two-fold rotational symmetry
* Square: vertical, horizontal, and diagonal reflection symmetry, and four-fold rotational symmetry
* T: vertical reflection symmetry only
* L: no symmetry
* S: two-fold rotational symmetry only

{{multiple image 
| align=left
| image_style = border:none;
| image_gap = 25
| image1 = Tetromino I Horizontal.svg
| width1=100
| caption1 = "straight tetromino"
| image2=Tetromino O Single.svg
| width2=50
| caption2= "square tetromino"
| image3=Tetromino T Up.svg
| width3=75
| caption3= "T-tetromino"
| image4=Tetromino L Up.svg
| width4=50
| caption4= "L-tetromino"
| image5=Tetromino S Horizontal.svg
| width5=75
| caption5= "skew tetromino"
}}
{{-}}

=== One-sided tetrominoes ===
One-sided tetrominoes are tetrominoes that may be translated and rotated but not reflected. They are used by, and are overwhelmingly associated with, ''[[Tetris]]''. There are seven distinct one-sided tetrominoes. These tetrominoes are named by the letter of the alphabet they most closely resemble. The "I", "O", and "T" tetrominoes have reflectional symmetry, so it does not matter whether they are considered as free tetrominoes or one-sided tetrominoes. The remaining four tetrominoes, "J", "L", "S", and "Z", exhibit a phenomenon called [[chirality (mathematics)|chirality]]. J and L are reflections of each other, and S and Z are reflections of each other.

As free tetrominoes, J is equivalent to L, and S is equivalent to Z, but in two dimensions and without reflections, it is not possible to transform J into L or S into Z.

{{multiple image 
| align=left
| image_style = border:none;
| image_gap = 25
| image1 = Tetromino I Horizontal.svg
| width1=100
| caption1 = I
| image2=Tetromino O Single.svg
| width2=50
| caption2=O
| image3=Tetromino T Up.svg
| width3=75
| caption3=T
| image4=Tetromino J Up.svg
| width4=50
| caption4=J
| image5=Tetromino L Up.svg
| width5=50
| caption5=L
| image6=Tetromino S Horizontal.svg
| width6=75
| caption6=S
| image7=Tetromino Z Horizontal.svg
| width7=75
| caption7=Z
}}
{{-}}

===Fixed tetrominoes===
The fixed tetrominoes allow only translation, not rotation or reflection. There are two distinct fixed I-tetrominoes, four J, four L, one O, two S, four T, and two Z, for a total of 19 fixed tetrominoes.

{{multiple image 
| align=left
| perrow=10
| image_style = border:none;
| image_gap = 10
| image1 = Tetromino J Up.svg
| width1=50
| image2= Tetromino J Left.svg
| width2=75
| image3= Tetromino J Down.svg
| width3=50
| image4= Tetromino J Right.svg
| width4=75
| image5= Tetromino S Horizontal.svg
| width5=75
| image6= Tetromino S Vertical.svg
| width6=50
| image7= Tetromino T Up.svg
| width7=75
| image8= Tetromino T Left.svg
| width8=50
| image9= Tetromino I Horizontal.svg
| width9=100
| image10= Tetromino O Single.svg
| width10=50
| image11 = Tetromino L Down.svg
| width11=50
| image12= Tetromino L Left.svg
| width12=75
| image13= Tetromino L Up.svg
| width13=50
| image14= Tetromino L Right.svg
| width14=75
| image15= Tetromino Z Horizontal.svg
| width15=75
| image16= Tetromino Z Vertical.svg
| width16=50
| image17= Tetromino T Down.svg
| width17=75
| image18= Tetromino T Right.svg
| width18=50
| image19= Tetromino I Vertical.svg
| width19=25
}}
{{-}}