Regular Complex PolytopesCUP Archive, 6 mars 1975 - 195 pages The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra. |
Table des matières
Unitary space | 8 |
83 | 12 |
6 | 64 |
Polyhedral kaleidoscopes | 72 |
The spherical torus | 79 |
The complete enumeration of finite reflection | 98 |
ΙΟΙ | 158 |
| 183 | |
Expressions et termes fréquents
angle appear belong called Cayley cells central centre Chapter circles complex consider consisting contains coordinates corresponding Coxeter defined denoted derived described determined diagram digon dihedral dimensions direct edges elements equal equation Euclidean EXERCISES expressed faces fact Figure finite group five follows four frieze pattern given half-turn honeycomb hyperplanes imply instance integers invariant inversion isometry joining lines matrices mirrors multiplied namely obtain opposite orthogonal orthoscheme P₁ pairs parallel particular period permutations perpendicular Petrie polygon plane points polygon polyhedron polytope presentation projection quaternion R₁ R₁ R₂ R₂ reciprocal reflection group reflections regarded regular regular polytope relations remaining replaced represented rotation satisfy shows sides Similarly space sphere spherical square subgroup surface symbol symmetry group tessellation Theorem transformation triangle u₁ unit unitary values vector vertex figure vertices whole yields