This preview shows page 1. Sign up to view the full content.
Unformatted text preview: three pairs of opposite edges. Take the three lines joining the centers of the pairs of opposite edges. These three lines are mutually orthogonal; they are the axes of a cartesian coordinate system. There are ve such coordinate systems that are permuted by the rotation group. Finally, given one such coordinate system, we can locate a cube whose faces are parallel to the coordinate planes and whose edges lie on the faces of the dodecahedron. Each edge of the cube is a diagonal of a face of the dodecahedron, and exactly one of the ve diagonals of each face is an edge of the cube. There are ve such cubes that are permuted by the rotation group. See Figure 4.2.5 on the next page . You are asked to show in Exercise 4.2.1 that the action of the rotation group on the set of ve inscribed cubes is faithful; that is, the homomor-phism of the rotation group into S 5 is injective....
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