Regular PolytopesCourier Corporation, 1 jan 1973 - 321 pagina's Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible. Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study. |
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a-form a₁ algebra analogous B₁ bounding hyperplanes cells centre Chapter circum-radius compound congruent transformation convex coordinates corresponding cos2 Coxeter cube cuboctahedron defined denote dihedral angle dodecahedron edges elements equal equation equatorial polygon equilateral Euclidean eutactic star faces finite groups follows formula four dimensions four-dimensional fundamental region geometry Gosset graph group of order half-turn hedron Hence honeycomb hyperplanes icosahedron infinite inscribed integers invariant lattice lines of symmetry Mathematical measure polytope mid-points n-dimensional N₁ N₂ nodes obtain occur octahedron orthogonal p-gon P₁ P₂ pairs parallel pentagonal permutations perpendicular Petrie polygon plane Platonic solids polyhedra projection R₁ R₂ reciprocal reflections regular polyhedron regular polytope rhombic rhombs rotation group Schläfli symbol Schoute sections segments semidefinite sides simplex space sphere star-polytopes stella octangula stellated subgroup surface symmetry group tetrahedron theorem theory tion triangles truncation vectors vertex figure zonohedron π π