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Unformatted text preview: 3) Associative Law : A(BC) = (AB)C Example: 1 + (2 + 3) = (1 + 2) + 3 4) Reciprocal Elements, S , Exist : X S = S X = E (the reciprocal of every positive integer is its negative) Key Point: Symmetry operations associated with an object form groups, so may be described and systematized using group theory. The Five Regular Polyhedra or Platonic Solids Symmetry operations: E , 8 C 3 , 6 C 2 , 6 C 4 , 3 C 2 (= C 4 2 ), i , 6 S 4 , 8 S 6 , 3 σ h , 6 d group order: 48 Symmetry operations: E , 8 C 3 , 3 C 2 , 6 S 4 , 6 d group order: 24 Tetrahedron ( T d ) Octahedron ( O h ) Icosahedron ( I h ) symmetry operations: E , 12 C 5 , 12 C 5 2 , 20 C 3 , 15 C 2 , i , 12 S 10 , 12 S 10 3 , 20 S 6 , 15 σ group order: 120...
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 Spring '09
 Tiley
 Group Theory, symmetry operations

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