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Quarter Hypercubic Honeycomb
In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of Honeycomb (geometry), honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q or Coxeter symbol qδ4 representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter diagram#Infinite Coxeter groups, Coxeter group _ for n ≥ 5, with _4 = _4 and for quarter n-cubic honeycombs _5 = _5.Coxeter, Regular and semi-regular honeycoms, 1988, p.318-319 See also * Hypercubic honeycomb * Alternated hypercubic honeycomb * Simplectic honeycomb * Truncated simplectic honeycomb * Omnitruncated simplectic honeycomb References * Coxeter, Coxeter, H.S.M. ''Regular Polytopes (book), Regular Polytopes'', (3rd edition, 1973), Dover edition, *# pp. 122–123, 1973. (The lattice of hypercubes γn form the ''cubic honeycombs'', δn+1) *# pp. 154–156: Partial truncation or alternation, represe ... [...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] |
