Unformatted text preview: 2 are any two symmetries, then their composition product ± 1 ± 2 is also a symmetry; and if the symmetries ± 1 and ± 2 are implemented by matrices F 1 and F 2 , then ± 1 ± 2 is implemented by the matrix product F 1 F 2 . So we can look for other symmetries by examining products of the matrices implementing the known symmetries. We have 14 matrices, so we can compute a lot of products before ﬁnding something new. If you are lucky, after a bit of trial and error you will discover that the combinations to try are powers of R multiplied by the reﬂection matrix J r :...
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 Fall '08
 EVERAGE
 Algebra, Addition, Multiplication, symmetries, 2 3 2 100 1 4 0 1 0 5 J, Jr D

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