Anagram & Information om | Engelska ordet COXETER

Exempel på hur man kan använda COXETER i en mening

• Many concepts in geometry and group theory are named after him, including the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm.
• Although the Weyl group is abstractly isomorphic to the Coxeter group, a specific isomorphism depends on an ordered choice of simple roots.
• Examples of infinite Coxeter groups include the triangle groups corresponding to regular tessellations of the Euclidean plane and the hyperbolic plane, and the Weyl groups of infinite-dimensional Kac–Moody algebras.
• The book came into the hands of Thomas Coxeter, and subsequently into those of Theophilus Cibber, furnishing the basis of the Lives of the Poets (1753) published with Cibber's name on the title page (though most of it was written by Robert Shiels).
• In this article Appel and Schupp introduced four theorems that are true about Coxeter groups and then proved them to be true for Artin groups.
• Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.
• The 29th dimension is the highest dimension for compact hyperbolic Coxeter polytopes that are bounded by a fundamental polyhedron, and the highest dimension that holds arithmetic discrete groups of reflections with noncompact unbounded fundamental polyhedra.
• The original work by Baker had been based on Gerard Langbaine's Account of the English Dramatick Poets (1691), Giles Jacob's Poetical Register (1719), Thomas Whincop's List of all the Dramatic Authors (printed with his tragedy of Scanderbeg, 1747) and the manuscripts of Thomas Coxeter.
• Below, the wallpaper group of the lattice is given in IUCr notation, Orbifold notation, and Coxeter notation, along with a wallpaper diagram showing the symmetry domains.
• Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.
• It lists the International Tables for Crystallography space group numbers, followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.
• Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.
• 151 is the number of uniform paracompact honeycombs with infinite facets and vertex figures in the third dimension, which stem from 23 different Coxeter groups.
• Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph.
• Which is the insphere? Important authorities such as Coxeter or Cundy & Rollett are clear enough that the face-tangent sphere is the insphere.
• Instead, Coxeter gave another proof of the Sylvester–Gallai theorem within ordered geometry, an axiomatization of geometry in terms of betweenness that includes not only Euclidean geometry but several other related geometries.
• Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram, with markup symbols for rotational and other subsymmetry point groups.
• The Coxeter plane is often used to draw diagrams of higher-dimensional polytopes and root systems – the vertices and edges of the polytope, or roots (and some edges connecting these) are orthogonally projected onto the Coxeter plane, yielding a Petrie polygon with -fold rotational symmetry.
• Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram, with markup symbols for rotational and other subsymmetry point groups.
• The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).

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