The group D4 of symmetries of a square is given by D4 = {I, R, R², R³, H, V, D, D'} where I is the identity, R is a clockwise rotation through 7/2, H and V are reflections in the horizontal and vertical, and D, D' are reflections in the diagonals y = x and y = -x respectively. [Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand 4 x 4 corner, and the main diagonal, are also quite easy. Then choose two or three other entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]
The group D4 of symmetries of a square is given by D4 = {I, R, R², R³, H, V, D, D'} where I is the identity, R is a clockwise rotation through 7/2, H and V are reflections in the horizontal and vertical, and D, D' are reflections in the diagonals y = x and y = -x respectively. [Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand 4 x 4 corner, and the main diagonal, are also quite easy. Then choose two or three other entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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draw the group tables for the following group:
![The group D4 of symmetries of a square is given by D4 = {1, R, R², R³, H, V, D, D'} where I
is the identity, R is a clockwise rotation through π/2, H and V are reflections in the horizontal
and vertical, and D, D' are reflections in the diagonals y = x and y = −x respectively.
[Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand
4 × 4 corner, and the main diagonal, are also quite easy. Then choose two or three other
entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F986f6c25-9d5d-4e3f-93bc-35b073c4428b%2F909a8617-d183-4f60-9c3a-7251cdf09ff0%2Fbvrj13_processed.png&w=3840&q=75)
Transcribed Image Text:The group D4 of symmetries of a square is given by D4 = {1, R, R², R³, H, V, D, D'} where I
is the identity, R is a clockwise rotation through π/2, H and V are reflections in the horizontal
and vertical, and D, D' are reflections in the diagonals y = x and y = −x respectively.
[Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand
4 × 4 corner, and the main diagonal, are also quite easy. Then choose two or three other
entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]
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