(ii) The group D4 of symmetries of a square is given by D₁ = {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!]
(ii) The group D4 of symmetries of a square is given by D₁ = {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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![(ii) 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 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!]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed029406-a1c1-473f-a3a0-6fd0fbd8e89d%2F419fd7aa-d698-4f03-81a1-87e1c97aa285%2Frxxk0mb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(ii) 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 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!]
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