College Algebra Exam Review 202

College Algebra Exam Review 202 - have accounted for all of...

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

View Full Document Right Arrow Icon
212 4. SYMMETRIES OF POLYHEDRA Figure 4.1.1. The regular polyhedra. R 3 . Furthermore, every symmetry permutes the vertices of the tetrahe- dron, by Exercise 1.4.7 , and fixes the center of mass of the tetrahedron, which is the average of the vertices. It follows that a symmetry also carries edges to edges and faces to faces. Using these facts, we can show that we
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: have accounted for all of the rotational symmetries. See Exercise 4.1.7 . The rotation group acts faithfully as permutations of the four vertices; this means there is an injective homomorphism of the rotation group into S 4 . Under this homomorphism the eight rotations of order 3 are mapped...
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.

Ask a homework question - tutors are online