About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 90. Chapters: Polygon, Polyhedron, Simplex, Dual polyhedron, Polytope, Polychoron, Hypercube, List of regular polytopes, Uniform polytope, Abstract polytope, Wythoff symbol, Oriented matroid, Truncation, Stellation, Convex polytope, Convex hull algorithms, Rectification, Demihypercube, Cross-polytope, Permutohedron, Semiregular k 21 polytope, Schlafli symbol, Alternation, Honeycomb, Hypercubic honeycomb, Vertex figure, Uniform 1 k2 polytope, Kleetope, Uniform 2 k1 polytope, Polytope families, Eutactic star, Petrie polygon, Complex polytope, Isogonal figure, Alternated hypercubic honeycomb, Birkhoff polytope, Wythoff construction, Net, Cauchy's theorem, Isotoxal figure, Vertex arrangement, Ehrhart polynomial, Bitruncation, Schlegel diagram, Expansion, Runcination, Gift wrapping algorithm, Polytope density, Isohedral figure, Integer points in convex polyhedra, List of polygons, polyhedra and polytopes, Facetting, Normal polytope, Cantellation, Convex lattice polytope, Cell, Extension of a polyhedron, Associahedron, Flag, Chiral polytope, Polytetrahedron, Hypercell, Edge, Edge figure, Dissection problem, Hyperrectangle, Peak, Polyhedral pyramid, Ridge. Excerpt: This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. The Schlafli symbol notation describes every regular polytope, and is used widely below as a compact reference name for each. The regular polytopes are grouped by dimension and subgrouped by convex, nonconvex and infinite forms. Nonconvex forms use the same vertices as the convex forms, but have intersecting facets. Infinite forms tessellate a one lower dimensional Euclidean space. Infinite forms can be extended to tessellate a hyperbolic space. Hyperbolic space is like normal space at a small scale, but parallel lines diverge at a distance. This allows vertex figures to have negative angle d...
