A chessboard (Fig. 7.1) has four plane symmetries, the identity e, rotation r through π about its centre, and the reflections q 1, q 2 in its two diagonals. They form a group under composition whose multiplication table is given below. It is easy to check that multiplication modulo eight makes the numbers 1, 3, 5, 7 into a group. Again we provide the corresponding table.
KeywordsSymmetry Group Plane Symmetry Rotational Symmetry Equilateral Triangle Proper Subgroup
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