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 reﬂection 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 threedimensional space that we have considered — the polygonal tiles, bricks, and the regular polyhedra — admit reﬂection symmetries. For “reasonable” ﬁgures, every symmetry is implemented by by a linear isometry of R 3 ; see Proposition 1.4.1 . The rotation...
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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

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