Rigid Motions (Isometries)

  • Vladimir Rovenski
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


Section 2.1 discusses the vectors and their use in analytic geometry. In Section 2.2 we study rigid motions of \({\mathbb{R}}^{n}\) (n≥2), including the complex and quaternionic approaches. Section 2.3 is devoted to the geometry on a sphere (induced by Euclidean geometry of the space), it and also introduces the stereographic projection. The study of polyhedra is organized in Section 2.4 in into the a sequence of themes: the notion of a polyhedron, Platonic solids, symmetries of geometrical figures, star-shaped polyhedra, and Archimedean solids. Section 2.5 (Appendix) surveys matrices and groups.


Symmetry Group Rigid Motion Convex Polyhedron Regular Polygon Simple Polygon 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of HaifaHaifaIsrael

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