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 ﬁnd two further unit vectors O v 2 and O v 3 such that the f O v i g form a right–handed orthonormal 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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 Fall '08
 EVERAGE
 Algebra, Determinant, Matrices, Polyhedron, Tetrahedron, Dual polyhedron, convex polyhedron, unit vector v1

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