College Algebra Exam Review 226

College Algebra Exam Review 226 - A 5 ² Z 2 Show that this...

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236 4. SYMMETRIES OF POLYHEDRA Figure 4.5.2. Snubcube. Exercises 4.5 4.5.1. Let G denote the full symmetry group of the cube and R the rotation group. The inversion i W x 7! x with matrix E is an element of G n R , so G D R [ R i . Observe that i 2 D 1 , and that for any rotation r , ir D ri . Conclude that G Š S 4 Z 2 . 4.5.2. Show that the same trick works for the dodecahedron, and that the full symmetry group is isomorphic to
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Unformatted text preview: A 5 ² Z 2 . Show that this group is not isomorphic to S 5 . 4.5.3. Show that the full symmetry group of the tetrahedron is S 4 . 4.5.4. What is the full symmetry group of a brick? 4.5.5. What is the full symmetry group of a square tile? 4.5.6. What is the full symmetry group of a tile in the shape of a regular n –gon?...
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