Unformatted text preview: hedron are isomorphic to the group of even permutations A 5 . Exercises 4.2 4.2.1. Show that no rotation of the dodecahedron leaves each of the ﬁve inscribed cubes ﬁxed. Thus the action of the rotation group on the set of inscribed cubes induces an injective homomorphism of the rotation group into S 5 . 4.2.2. Let A D f 2 4 cos 2k±=5 sin 2k±=5 1=2 3 5 W 1 ± k ± 5 g and B D f 2 4 cos .2k C 1/±=5 sin .2k C 1/±=5 ² 1=2 3 5 W 1 ± k ± 5 g :...
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 Fall '08
 EVERAGE
 Algebra, Permutations, 2k, 5g, 5 5 W, Rotation group

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