This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2 . (d) Show that any rotation matrix R is a product of two reection matrices. 4.4.5. Show that an element of SO . 3 ; R / is a product of two reection matrices. A matrix of a rotationreection is a product of three reec-tion matrices. Thus any element of O . 3 ; R / is a product of at most three reection matrices. 4.5. The Full Symmetry Group and Chirality All the geometric gures in three-dimensional space that we have con-sidered the polygonal tiles, bricks, and the regular polyhedra admit reection symmetries. For reasonable gures, every symmetry is imple-mented by by a linear isometry of R 3 ; see Proposition 1.4.1 . The rotation...
View Full Document
- Fall '08