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Unformatted text preview: ngon are r k j for k D 0;1;:::;n ± 1 . 2.3.5. (a) Show that if n is odd, then the axis of each of the “ﬂips” passes through a vertex of the ngon and the midpoint of the opposite edge. See Figure 2.3.2 on page 107 for the case n D 5 . (b) If n is even and k is even, show that j k±=n D r k j is a rotation about an axis passing through a pair of opposite vertices of the ngon. (c) Show that if n is even and k is odd, then j k±=n D r k j is a rotation about an axis passing through the midpoints of a pair of opposite edges of the ngon. See Figure 2.3.2 on page 107 for the case n D 6 . 2.3.6. Find a subgroup of D 6 that is isomorphic to D 3 . 2.3.7. Find a subgroup of D 6 that is isomorphic to the symmetry group of the rectangle....
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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.
 Fall '08
 EVERAGE
 Algebra

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