College Algebra Exam Review 202

# College Algebra Exam Review 202 - have accounted for all of...

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212 4. SYMMETRIES OF POLYHEDRA Figure 4.1.1. The regular polyhedra. R 3 . Furthermore, every symmetry permutes the vertices of the tetrahe- dron, by Exercise 1.4.7 , and ﬁxes the center of mass of the tetrahedron, which is the average of the vertices. It follows that a symmetry also carries edges to edges and faces to faces. Using these facts, we can show that we
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Unformatted text preview: have accounted for all of the rotational symmetries. See Exercise 4.1.7 . The rotation group acts faithfully as permutations of the four vertices; this means there is an injective homomorphism of the rotation group into S 4 . Under this homomorphism the eight rotations of order 3 are mapped...
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## This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.

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