College Algebra Exam Review 203

College Algebra Exam Review 203 - Let us also work out the...

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4.1. ROTATIONS OF REGULAR POLYHEDRA 213 Figure 4.1.2. Three-fold axis of the tetrahedron. Figure 4.1.3. Two–fold axis of the tetrahedron. to the eight 3–cycles in S 4 . The three rotations of order 2 are mapped to the three elements .12/.34/;.13/.24/ , and .14/.23/ . Thus the image in S 4 is precisely the group of even permutations A 4 . Proposition 4.1.2. The rotation group of the tetrahedron is isomorphic to the group A 4 of even permutations of four objects.
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Unformatted text preview: Let us also work out the matrices that implement the rotations of the tetrahedron. First we need to figure out how to write the matrix for a rotation through an angle ± about the axis determined by a unit vector O v . Of course, there are two possible such rotations, which are inverses of each other; let’s agree to find the one determined by the “right–hand rule,” as in Figure 4.1.4 on the next page ....
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