College Algebra Exam Review 203

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Let us also work out the matrices that implement the rotations of the tetrahedron. First we need to gure 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; lets agree to nd the one determined by the righthand rule, as in Figure 4.1.4 on the next page ....
View Full Document

Ask a homework question - tutors are online