Unformatted text preview: Figure 2.3.2 for the case n D 5 . 5. If n is even and k is even, then j k±=n D r k j is a ﬂip about an axis passing through a pair of opposite vertices of the n-gon. 6. If n is even and k is odd, then j k±=n D r k j is a ﬂip about an axis passing through the midpoints of a pair of opposite edges of the n-gon. See Figure 2.3.2 for the case n D 6 . rj j r j rj r Figure 2.3.2. Symmetries of the pentagon and hexagon. The symmetry group D n consists of the 2n symmetries r k and r k j , for ² k ² n ± 1 . It follows from our computations for the symmetries of the disk that jr D r ± 1 j , so jr k D r ± k j for all k . This relation allows the computation of all products in D n ....
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- Fall '08
- Algebra, NJ, Symmetry group, Regular polygon, symmetries, distinct ﬂip symmetries