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
.