Unformatted text preview: of the cube very easily. Note that the 3–fold axes for the tetrahedron are also 3–fold axes for the cube, and the 2–fold axes for the tetrahedron are 4–fold axes for the cube. In particular, the symmetries of the tetrahedron form a subgroup of the symmetries of the cube of index 2. Using these considerations, we obtain the following result; see Exercise 4.1.5 . Proposition 4.1.5. The group of rotation matrices of the cube is isomorphic to the group of 3–by–3 signed permutation matrices with determinant 1. This group is the semidirect product of the group of order 4 consisting of diagonal signed permutation matrices with determinant 1, and the group of 3–by–3 permutation matrices....
View
Full
Document
This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

Click to edit the document details