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Omnitruncated 5-cell Prism
In geometry, an omnitruncation is an operation applied to a regular polytope (or Honeycomb (geometry), honeycomb) in a Wythoff construction that creates a maximum number of Facet (geometry), facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a ''shortcut'' term which has a different meaning in progressively-higher-dimensional polytopes: * Uniform polytope#Truncation_operators, Uniform polytope truncation operators ** For regular polygons: Truncation (geometry), An ordinary truncation, t_\ = t\ = \. *** Coxeter-Dynkin diagram ** For Uniform polyhedron, uniform polyhedra (3-polytopes): Uniform polyhedron#Definition of operations, A cantitruncation, t_\ = tr\. (Application of both cantellation and truncation operations) *** Coxeter-Dynkin diagram: ** For uniform 4-polytope, uniform polychora: Uniform 4-polytope#Geometric derivations for 46 nonprismatic Wythoffian uniform 4-polytopes, A runcicantitruncation, t_\. (Application of runcination, cantel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
