College Algebra Exam Review 208

College Algebra Exam Review 208 - The octahedron is dual to...

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218 4. SYMMETRIES OF POLYHEDRA Corollary 4.1.6. S 4 is isomorphic to the group of 3–by–3 signed permu- tation matrices with determinant 1. Each convex polyhedron T has a dual polyhedron whose vertices are at the centroids of the faces of T ; two vertices of the dual are joined by an edge if the corresponding faces of T are adjacent. The dual polyhedron has the same symmetry group as does the original polyhedron. Proposition 4.1.7.
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Unformatted text preview: The octahedron is dual to the cube, so its group of rotations is also isomorphic to S 4 (Figure 4.1.10 ). Figure 4.1.10. Cube and octahedron. Exercises 4.1 4.1.1. (a) Given a unit vector O v 1 , explain how to nd two further unit vec-tors O v 2 and O v 3 such that the f O v i g form a righthanded orthonor-mal basis. (b) Carry out the procedure for O v 1 D .1= p 3/ 2 4 1 1 1 3 5 :...
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