We can form a symmetry group by using rotations of a square rather than a triangle. Start with a square with corners lab
Posted: Mon Jul 11, 2022 12:46 pm
We can form a symmetry group by using rotations of a squarerather than a triangle. Start with a square with corners labeled 1through 4, placed in a reference square.
The current position of the inner square islabeled I. We can rotate the inner square clockwise90° to give an element of thegroup, R90. Similarly, we can rotate thesquare 180° or 270° to obtain theelements R180 and R270.In addition, we can rotate the square about any of the lines ofsymmetry shown below.
The operation "followed by," is denoted by Δ. The followingexercise refers to this symmetry group of the square.Find
RhΔR270.
RhΔR270 =
The current position of the inner square islabeled I. We can rotate the inner square clockwise90° to give an element of thegroup, R90. Similarly, we can rotate thesquare 180° or 270° to obtain theelements R180 and R270.In addition, we can rotate the square about any of the lines ofsymmetry shown below.
The operation "followed by," is denoted by Δ. The followingexercise refers to this symmetry group of the square.Find
RhΔR270.
RhΔR270 =