Unformatted text preview: ² 2 . (d) Show that any rotation matrix R ² is a product of two reﬂection matrices. 4.4.5. Show that an element of SO . 3 ; R / is a product of two reﬂection matrices. A matrix of a rotation–reﬂection is a product of three reﬂec-tion matrices. Thus any element of O . 3 ; R / is a product of at most three reﬂection matrices. 4.5. The Full Symmetry Group and Chirality All the geometric ﬁgures in three-dimensional space that we have con-sidered — the polygonal tiles, bricks, and the regular polyhedra — admit reﬂection symmetries. For “reasonable” ﬁgures, every symmetry is imple-mented by by a linear isometry of R 3 ; see Proposition 1.4.1 . The rotation...
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