Math 105 Problem Solution
Symmetry Group of a Square
I = Identity
R90 = Rotation by 90 degrees clockwise.
R180 = Rotation by 180 degrees clockwise.
R270 = Rotation by 270 degrees clockwise.
H = reflection on Horizontal line.
V = reflection on Vertical line.
X = reflection on SW to NE Line.
Y = reflection on NW to SE Line
|
I
|
R90
|
R180
|
R270
|
H
|
V
|
X
|
Y
|
I
|
I
|
R90
|
R180
|
R270
|
H
|
V
|
X
|
Y
|
R90
|
R90
|
R180
|
R270
|
I
|
X
|
Y
|
H
|
V
|
R180
|
R180
|
R270
|
I
|
R90
|
V
|
H
|
Y
|
X
|
R270
|
R270
|
I
|
R90
|
R180
|
Y
|
X
|
V
|
H
|
H
|
H
|
Y
|
V
|
X
|
I
|
R180
|
R90
|
R270
|
V
|
V
|
X
|
H
|
Y
|
R180
|
I
|
R270
|
R90
|
X
|
X
|
V
|
Y
|
H
|
R270
|
R90
|
I
|
R180
|
Y
|
Y
|
H
|
X
|
V
|
R90
|
R270
|
R180
|
I
|
.