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

.