Name: Problem of the Day #14

1. Cayley Table for the Symmetries of the Square. Consider the eight symmetries of the square as follows:

a. I (identity)

b. R1 (90 degree counterclockwise rotation)

c. R2 (180 degree counterclockwise rotation)

d. R3 (270 degree counterclockwise rotation)

e. V (reflection across the vertical center line)

f. H (reflection across the horizontal center line)

g. D1 (reflection across the “back-slash” diagonal)

h. D2 (reflection across the “forward-slash” diagonal)

Using these labels for these symmetries of the square, complete the following Cayley Table for this symmetry group. Remember that “I o R3” would be written in the cell along the row labeled I and the column labeled R3 and in that space you would give the single transformation that is equivalent to doing R3 first following by I.

o	I	R1	R2	R3	V	H	D1	D2
I
R1
R2
R3
V
H
D1
D2