number of vertices: 5 dimension: 3 group order: 12 1 elements of order 1 7 elements of order 2 2 elements of order 3 2 elements of order 6 #0 group element of order 1: ( 0 )( 1 )( 2 )( 3 )( 4 ) space representation: 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvectors: 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: 1.0000 1.0000 1.0000 #1 group element of order 2: ( 0 )( 1 )( 2 )( 3 4 ) space representation: 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 -1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvectors: 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: 1.0000 -1.0000 1.0000 #2 group element of order 2: ( 0 )( 1 )( 2 3 )( 4 ) space representation: -0.5000000000000000 0.8660254075688774 0.0000000000000000 0.8660253999999999 0.5000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvectors: 0.5000000016387099 -0.8660254047305483 0.0000000000000000 0.8660254028383290 0.4999999983612898 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: 1.0000 -1.0000 1.0000 #3 group element of order 3: ( 0 )( 1 )( 2 3 4 ) space representation: -0.5000000000000000 -0.8660254075688774 0.0000000000000000 0.8660253999999999 -0.5000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvectors: 0.7071067827315382 0.0000000000000000 0.0000000000000000 0.0000000000000000 -0.7071067796415569 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: -0.5000 + 0.8660 i (angle = 120.0000 ) -0.5000 - 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0.8660 i (angle = -120.0000 ) -1.0000 #10 group element of order 6: ( 0 1 )( 2 4 3 ) space representation: -0.5000000000000000 0.8660254075688774 0.0000000000000000 -0.8660253999999999 -0.5000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 -1.0000000000000000 eigenvectors: 0.7071067827315382 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.7071067796415569 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: -0.5000 + 0.8660 i (angle = 120.0000 ) -0.5000 - 0.8660 i (angle = -120.0000 ) -1.0000 #11 group element of order 2: ( 0 1 )( 2 4 )( 3 ) space representation: -0.5000000000000000 -0.8660254075688774 0.0000000000000000 -0.8660253999999999 0.5000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 -1.0000000000000000 eigenvectors: 0.8660254047305482 -0.5000000016387102 0.0000000000000000 0.4999999983612902 0.8660254028383289 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000 eigenvalues: -1.0000 1.0000 -1.0000