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COXETER GRAPH

  • Coxeter graph
  • Cubic graph with 28 vertices and 42 edges

    field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is

    Coxeter graph

    Coxeter graph

    Coxeter_graph

  • Coxeter group
  • Group that admits a formal description in terms of reflections

    is a Coxeter matrix. The Coxeter matrix can be conveniently encoded by a Coxeter diagram, as per the following rules. The vertices of the graph are labelled

    Coxeter group

    Coxeter_group

  • Harold Scott MacDonald Coxeter
  • Canadian geometer (1907–2003)

    the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was

    Harold Scott MacDonald Coxeter

    Harold Scott MacDonald Coxeter

    Harold_Scott_MacDonald_Coxeter

  • Tutte–Coxeter graph
  • 3-regular graph with 30 vertices and 45 edges

    mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45

    Tutte–Coxeter graph

    Tutte–Coxeter graph

    Tutte–Coxeter_graph

  • Coxeter–Dynkin diagram
  • Pictorial representation of symmetry

    a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group

    Coxeter–Dynkin diagram

    Coxeter–Dynkin diagram

    Coxeter–Dynkin_diagram

  • Heawood graph
  • Undirected graph with 14 vertices

    "From the Coxeter graph to the Klein graph", Journal of Graph Theory, 70: 1–9, arXiv:1002.1960, doi:10.1002/jgt.20597, S2CID 754481. Coxeter (1950), "Self-dual

    Heawood graph

    Heawood graph

    Heawood_graph

  • Petersen graph
  • Cubic graph with 10 vertices and 15 edges

    Petersen graph. Only five connected vertex-transitive graphs with no Hamiltonian cycles are known: the complete graph K2, the Petersen graph, the Coxeter graph

    Petersen graph

    Petersen graph

    Petersen_graph

  • Goldberg–Coxeter construction
  • Graph operation

    Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs with

    Goldberg–Coxeter construction

    Goldberg–Coxeter construction

    Goldberg–Coxeter_construction

  • Simplicial honeycomb
  • Tiling of n-dimensional space

    {\displaystyle {\tilde {A}}_{n}} affine Coxeter group symmetry. It is represented by a Coxeter-Dynkin diagram as a cyclic graph of n + 1 nodes with one node ringed

    Simplicial honeycomb

    Simplicial honeycomb

    Simplicial_honeycomb

  • List of graphs
  • graph Coxeter graph Tutte–Coxeter graph Dyck graph Klein graph Foster graph Biggs–Smith graph The Rado graph Folkman graph Gray graph Ljubljana graph Tutte

    List of graphs

    List_of_graphs

  • Gosset graph
  • Distance-regular graph with 56 vertices

    vertex in the Gosset graph is isomorphic to the Schläfli graph. The automorphism group of the Gosset graph is isomorphic to the Coxeter group E7 and hence

    Gosset graph

    Gosset graph

    Gosset_graph

  • Schreier coset graph
  • Construction in combinatorial group theory

    The graph is named after Otto Schreier, who used the term "Nebengruppenbild". An equivalent definition was made in an early paper of Todd and Coxeter. Given

    Schreier coset graph

    Schreier_coset_graph

  • Klein graphs
  • Two special graphs in graph theory

    Klein graph, referenced as F056B, is the only cubic symmetric graph on 56 vertices which is not bipartite. It can be derived from the 28-vertex Coxeter graph

    Klein graphs

    Klein graphs

    Klein_graphs

  • Cubic graph
  • Graph with all vertices of degree 3

    the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T. Tutte

    Cubic graph

    Cubic graph

    Cubic_graph

  • Generalized Petersen graph
  • Family of cubic graphs formed from regular and star polygons

    by H. S. M. Coxeter and was given its name in 1969 by Mark Watkins. In Watkins' notation, G ( n , k ) {\displaystyle G(n,k)} is a graph with vertex set

    Generalized Petersen graph

    Generalized Petersen graph

    Generalized_Petersen_graph

  • Distance-regular graph
  • Graph property

    Cubical graph, the Heawood graph, the Pappus graph, the Coxeter graph, the Tutte–Coxeter graph, the Dodecahedral graph, the Desargues graph, Tutte 12-cage

    Distance-regular graph

    Distance-regular_graph

  • Moore graph
  • Regular graph with girth more than twice its diameter

    the complete bipartite graphs Kn,n with girth four, the Heawood graph with degree 3 and girth 6, and the Tutte–Coxeter graph with degree 3 and girth

    Moore graph

    Moore_graph

  • Distance-transitive graph
  • Graph where any two nodes of equal distance are isomorphic

    In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any

    Distance-transitive graph

    Distance-transitive graph

    Distance-transitive_graph

  • McKay graph
  • Construction in graph theory

    Coxeter elements", Pacific Journal of Mathematics, 18: 587–598, doi:10.2140/pjm.1985.118.587 McKay, John (1982), "Representations and Coxeter Graphs"

    McKay graph

    McKay graph

    McKay_graph

  • Crossing number (graph theory)
  • Fewest edge crossings in drawing of a graph

    graphs include the Nauru graph and the McGee graph or (3,7)-cage graph, with 24 vertices. The smallest 11-crossing cubic graphs include the Coxeter graph

    Crossing number (graph theory)

    Crossing number (graph theory)

    Crossing_number_(graph_theory)

  • Girth (graph theory)
  • Length of a shortest cycle contained in the graph

    girth of 7 The Tutte–Coxeter graph (Tutte eight cage) has a girth of 8 For any positive integers g and χ, there exists a graph with girth at least g

    Girth (graph theory)

    Girth_(graph_theory)

  • LCF notation
  • Representation of cubic graphs

    mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht

    LCF notation

    LCF notation

    LCF_notation

  • Regular dodecahedron
  • Solid with 12 equal pentagonal faces

    represented as a graph, and it is called the dodecahedral graph, a Platonic graph. This graph can also be constructed as the generalized Petersen graph G ( 10

    Regular dodecahedron

    Regular dodecahedron

    Regular_dodecahedron

  • Goursat tetrahedron
  • angle. A 4-node Coxeter-Dynkin diagram represents this tetrahedral graph with order-2 edges hidden. If many edges are order 2, the Coxeter group can be represented

    Goursat tetrahedron

    Goursat tetrahedron

    Goursat_tetrahedron

  • Cremona–Richmond configuration
  • is a generalized quadrangle with parameters (2,2). Its Levi graph is the Tutte–Coxeter graph. The points of the Cremona–Richmond configuration may be identified

    Cremona–Richmond configuration

    Cremona–Richmond configuration

    Cremona–Richmond_configuration

  • Cyclotruncated simplicial honeycomb
  • {A}}_{n}} affine Coxeter group. It is given a Schläfli symbol t0,1{3[n+1]}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of n+1 nodes

    Cyclotruncated simplicial honeycomb

    Cyclotruncated simplicial honeycomb

    Cyclotruncated_simplicial_honeycomb

  • Regular octahedron
  • Solid with eight equal triangular faces

    octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example of a four-connected

    Regular octahedron

    Regular octahedron

    Regular_octahedron

  • Lovász conjecture
  • Problem in graph theory

    complete graph K 2 {\displaystyle K_{2}} , the Petersen graph, the Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing

    Lovász conjecture

    Lovász_conjecture

  • Hoffman–Singleton graph
  • 7-regular undirected graph with 50 nodes and 175 edges

    Singleton graph also contains the odd graph O(4), the Coxeter graph, and the Tutte-Coxeter graph as subgraphs. Take any edge of the Hoffman-Singleton graph, and

    Hoffman–Singleton graph

    Hoffman–Singleton graph

    Hoffman–Singleton_graph

  • Graph theory
  • Area of discrete mathematics

    lines". The Coxeter Legacy. Providence, RI: American Mathematical Society. pp. 179–225. MR 2209028. Hahn, Geňa; Tardif, Claude (1997). "Graph homomorphisms:

    Graph theory

    Graph theory

    Graph_theory

  • Symmetric graph
  • Graph in which all ordered pairs of linked nodes are automorphic

    In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )

    Symmetric graph

    Symmetric graph

    Symmetric_graph

  • Italo Jose Dejter
  • Argentine-born American mathematician

    that the 56-vertex Klein cubic graph F{56}B, denoted here Γ', can be obtained from the 28-vertex Coxeter cubic graph Γ by zipping adequately the squares

    Italo Jose Dejter

    Italo Jose Dejter

    Italo_Jose_Dejter

  • Dynkin diagram
  • Pictorial representation of symmetry

    blank in the upper right, corresponding to directed graphs with underlying undirected graph any Coxeter diagram (of a finite group), can be defined formally

    Dynkin diagram

    Dynkin diagram

    Dynkin_diagram

  • ADE classification
  • Mathematical classification

    ISBN 978-0-8218-1440-6 McKay, John (1982), "Representations and Coxeter Graphs", "The Geometric Vein", Coxeter Festschrift, Berlin: Springer-Verlag, pp. 549– Kac,

    ADE classification

    ADE classification

    ADE_classification

  • 5
  • Natural number

    hyperbolic Coxeter groups, or 4-prisms, of rank 5, each generating uniform honeycombs in hyperbolic 4-space as permutations of rings of the Coxeter diagrams

    5

    5

  • Tesseract
  • Four-dimensional analogue of the cube

    and The Twilight Zone). Penguin Books. p. 143. Coxeter 1970, p. 18. Pournin, Lionel (2013). "The flip-Graph of the 4-dimensional cube is connected". Discrete

    Tesseract

    Tesseract

    Tesseract

  • Complete bipartite graph
  • Bipartite graph where each node of 1st set is linked to all nodes of 2nd set

    In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first

    Complete bipartite graph

    Complete bipartite graph

    Complete_bipartite_graph

  • Truncated icosidodecahedron
  • Archimedean solid with 62 faces

    Archimedean graph. This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram

    Truncated icosidodecahedron

    Truncated icosidodecahedron

    Truncated_icosidodecahedron

  • Bitangents of a quartic
  • 28 lines which touch a general quartic plane curve in two places

    Manivel (2006). Dejter, Italo J. (2011), "From the Coxeter graph to the Klein graph", Journal of Graph Theory, 70: 1–9, arXiv:1002.1960, doi:10.1002/jgt

    Bitangents of a quartic

    Bitangents of a quartic

    Bitangents_of_a_quartic

  • Cage (graph theory)
  • Regular graph with fewest possible nodes for its girth

    Heawood graph, 14 vertices (3,7)-cage: the McGee graph, 24 vertices (3,8)-cage: the Tutte–Coxeter graph, 30 vertices (3,10)-cage: the Balaban 10-cage, 70

    Cage (graph theory)

    Cage (graph theory)

    Cage_(graph_theory)

  • Zero-symmetric graph
  • this class of graphs was coined by R. M. Foster in a 1966 letter to H. S. M. Coxeter. In the context of group theory, zero-symmetric graphs are also called

    Zero-symmetric graph

    Zero-symmetric graph

    Zero-symmetric_graph

  • Rhombicosidodecahedron
  • Archimedean solid with 62 faces

    triangles, squares, and pentagons. The last two correspond to the A2 and H2 Coxeter planes. The rhombicosidodecahedron can also be represented as a spherical

    Rhombicosidodecahedron

    Rhombicosidodecahedron

    Rhombicosidodecahedron

  • Petrie polygon
  • Skew polygon derived from a polytope

    question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is the Coxeter number of the Coxeter group. These polygons

    Petrie polygon

    Petrie polygon

    Petrie_polygon

  • Bruhat order
  • Partial order on a Coxeter group

    permutations. The Bruhat graph is a directed graph related to the (strong) Bruhat order. The vertex set is the set of elements of the Coxeter group and the edge

    Bruhat order

    Bruhat_order

  • Regular icosahedron
  • Solid with twenty equal triangular faces

    of Graph Theory. American Mathematical Society. ISBN 978-1-4704-5549-1. Borovik, Alexandre (2006). Davis, Chandler; Ellers, Erich (eds.). Coxeter Theory:

    Regular icosahedron

    Regular icosahedron

    Regular_icosahedron

  • W. T. Tutte
  • British-Canadian codebreaker and mathematician (1917–2002)

    fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable importance. At a time when graph theory

    W. T. Tutte

    W._T._Tutte

  • 5-cube
  • 5-dimensional hypercube

    n-cube Coxeter plane projections in the Bk Coxeter groups project into k-cube graphs, with power of two vertices overlapping in the projective graphs. The

    5-cube

    5-cube

  • Cayley graph
  • Graph defined from a mathematical group

    In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract

    Cayley graph

    Cayley graph

    Cayley_graph

  • E9 honeycomb
  • There are no regular honeycombs in the family since its Coxeter diagram is a nonlinear graph, but there are three simplest ones, with a single ring at

    E9 honeycomb

    E9_honeycomb

  • Levi graph
  • Graph representing incident points and lines

    Ljubljana graph on 112 vertices is the Levi graph of the Ljubljana configuration. Grünbaum, Branko (2006). "Configurations of points and lines". The Coxeter Legacy

    Levi graph

    Levi graph

    Levi_graph

  • Tetrahedron
  • Polyhedron with four faces

    tetrahedra. Coxeter 1973, pp. 292–293, Table I(i); "Tetrahedron, 𝛼3". Coxeter 1973, pp. 33–34, §3.1 Congruent transformations. Coxeter 1973, p. 63,

    Tetrahedron

    Tetrahedron

    Tetrahedron

  • 5-demicube
  • Regular 5-polytope

    as HM5 for a 5-dimensional half measure polytope. Coxeter named this polytope as 121 from its Coxeter diagram, which has branches of length 2, 1 and 1

    5-demicube

    5-demicube

    5-demicube

  • Paracompact uniform honeycombs
  • Tessellation of convex uniform polyhedron cells

    = . Removing a mirror from some of the cyclic hyperbolic Coxeter graphs become bow-tie graphs: [(3,3,4,1+,4)] = [((3,∞,3)),((3,∞,3))] or , [(3,4,4,1+,4)]

    Paracompact uniform honeycombs

    Paracompact_uniform_honeycombs

  • Cube
  • Solid with six equal square faces

    drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube

    Cube

    Cube

    Cube

  • Regular map (graph theory)
  • Symmetric tessellation of a closed surface

    Topological graph theory Abstract polytope Planar graph Toroidal graph Graph embedding Regular tiling Platonic solid Platonic graph Nedela (2007) Coxeter & Moser

    Regular map (graph theory)

    Regular map (graph theory)

    Regular_map_(graph_theory)

  • Coxeter notation
  • Classification system for symmetry groups in geometry

    Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter

    Coxeter notation

    Coxeter notation

    Coxeter_notation

  • Laves graph
  • Periodic spatial graph

    an abstract undirected graph, a covering graph of the complete graph on four vertices. H. S. M. Coxeter (1955) named this graph after Fritz Laves, who

    Laves graph

    Laves graph

    Laves_graph

  • Uniform 4-polytope
  • Class of 4-dimensional polytopes

    Honeycombs under advisor Coxeter, completes the basic theory of uniform polytopes for dimensions 4 and higher. 1986 Coxeter published a paper Regular

    Uniform 4-polytope

    Uniform 4-polytope

    Uniform_4-polytope

  • Nauru graph
  • 24-vertex symmetric bipartite cubic graph

    In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David

    Nauru graph

    Nauru graph

    Nauru_graph

  • Hamiltonian path
  • Path in a graph that visits each vertex exactly once

    as a graph, is Hamiltonian The Cayley graph of a finite Coxeter group is Hamiltonian (see Lovász conjecture for a more general claim) Cayley graphs on nilpotent

    Hamiltonian path

    Hamiltonian path

    Hamiltonian_path

  • Herschel graph
  • Bipartite non-Hamiltonian polyhedral graph

    In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the

    Herschel graph

    Herschel graph

    Herschel_graph

  • Graph of a polytope
  • {\displaystyle H(2,3)} . The Bruhat graph is the edge graph of the permutahedron. More generally, the Cayley graph of a finite Coxeter group (with the natural generators)

    Graph of a polytope

    Graph of a polytope

    Graph_of_a_polytope

  • List of unsolved problems in mathematics
  • combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Vaughan Jones
  • New Zealand mathematician and Fields Medalist

    Goodman, Frederick M.; de la Harpe, Pierre; Jones, Vaughan F. R. (1989). Coxeter graphs and towers of algebras. Mathematical Sciences Research Institute Publications

    Vaughan Jones

    Vaughan Jones

    Vaughan_Jones

  • List of graphs by edges and vertices
  • the graph is planar and F indicates that the graph is not planar. Wikimedia Commons has media related to Graphs by number of vertices. See also Graph theory

    List of graphs by edges and vertices

    List_of_graphs_by_edges_and_vertices

  • Regular skew apeirohedron
  • Infinite regular skew polyhedron

    and dual {2r,2q|p}. For the special case of linear graph groups r = 2, this represents the Coxeter group [p,q,p]. It generates regular skews {2q,4|p}

    Regular skew apeirohedron

    Regular skew apeirohedron

    Regular_skew_apeirohedron

  • Jacques Tits
  • Belgian mathematician (1930–2021)

    he helped popularize H.S.M. Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph. Tits died on 5 December 2021

    Jacques Tits

    Jacques Tits

    Jacques_Tits

  • Möbius–Kantor graph
  • Symmetric bipartite cubic graph with 16 vertices and 24 edges

    The Möbius–Kantor graph is a double cover of the graph of the cube. Pauli group, whose Cayley graph is the Möbius–Kantor graph Coxeter 1950. OEIS sequence

    Möbius–Kantor graph

    Möbius–Kantor graph

    Möbius–Kantor_graph

  • Cuboctahedron
  • Polyhedron with 8 triangles and 6 squares

    Williams 1979, p. 74. Coxeter 1973, p. 69, §4.7 Other honeycombs. Coxeter 1973, pp. 292–293, Table I (ii): column 0R/l. Coxeter 1973, p. 296, Table II:

    Cuboctahedron

    Cuboctahedron

    Cuboctahedron

  • Uniform 5-polytope
  • Five-dimensional geometric shape

    Coxeter in his publication Regular and Semi-Regular Polytopes I, II, and III. 1966: Norman W. Johnson completed his Ph.D. dissertation under Coxeter,

    Uniform 5-polytope

    Uniform 5-polytope

    Uniform_5-polytope

  • Truncated icosahedron
  • Polyhedron resembling a soccerball

    represented as a polyhedral graph, meaning a planar graph (one that can be drawn without crossing edges) and 3-vertex-connected graph (remaining connected whenever

    Truncated icosahedron

    Truncated icosahedron

    Truncated_icosahedron

  • Uniform 7-polytope
  • Seven-dimensional geometric object

    for Coxeter plane graphs of these polytopes. The E7 Coxeter group has order 2,903,040. There are 127 forms based on all permutations of the Coxeter-Dynkin

    Uniform 7-polytope

    Uniform 7-polytope

    Uniform_7-polytope

  • 4 21 polytope
  • Polytope in 8-dimensional geometry

    He called it an 8-ic semi-regular figure. Its Coxeter symbol is 421, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end

    4 21 polytope

    4 21 polytope

    4_21_polytope

  • Table of simple cubic graphs
  • Constructs with triply-connected vertices

    Euclidean and graph theoretic distance, placed in a Molfile, then rendered by Jmol.) The LCF notation is a notation by Joshua Lederberg, Coxeter and Frucht

    Table of simple cubic graphs

    Table_of_simple_cubic_graphs

  • Pentellated 6-simplexes
  • Uniform 6-polytope

    6-simplex honeycomb. Note: (*) Symmetry doubled for Ak graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram. This configuration matrix represents

    Pentellated 6-simplexes

    Pentellated 6-simplexes

    Pentellated_6-simplexes

  • 5-cell
  • Four-dimensional analogue of the tetrahedron

    pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's α4 polytope), the simplest possible convex 4-polytope, and is analogous

    5-cell

    5-cell

    5-cell

  • 7-cube
  • 7-dimensional hypercube

    6-simplex 6-faces. Coxeter, Regular Polytopes, p. 12, Sec. 1.8 Configurations Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes

    7-cube

    7-cube

    7-cube

  • 3 21 polytope
  • Uniform 7-dimensional polytope

    polytope is the Gosset graph. This polytope, along with the 7-simplex, can tessellate 7-dimensional space, represented by 331 and Coxeter-Dynkin diagram: .

    3 21 polytope

    3 21 polytope

    3_21_polytope

  • Coxeter element
  • Concept in geometry

    In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the

    Coxeter element

    Coxeter_element

  • 2 21 polytope
  • Uniform 6-polytope

    (Paper 17) Coxeter, The Evolution of Coxeter-Dynkin diagrams, [Nieuw Archief voor Wiskunde 9 (1991) 233–248], Figure 1: (p. 232) (Node-edge graph of polytope)

    2 21 polytope

    2 21 polytope

    2_21_polytope

  • Truncated tetrahedron
  • Archimedean solid with 8 faces

    World Cup. In the mathematical field of graph theory, a truncated tetrahedral graph is an Archimedean graph, the graph of vertices and edges of the truncated

    Truncated tetrahedron

    Truncated tetrahedron

    Truncated_tetrahedron

  • Clebsch graph
  • One of two different regular graphs with 16 vertices

    graph determined by its spectrum. The 5-regular Clebsch graph is a Cayley graph with an automorphism group of order 1920, isomorphic to the Coxeter group

    Clebsch graph

    Clebsch graph

    Clebsch_graph

  • Four color theorem
  • Planar maps require at most four colors

    terms of graph theory, by considering it in terms of constructing a graph coloring of the planar graph of adjacencies between regions. In graph-theoretic

    Four color theorem

    Four color theorem

    Four_color_theorem

  • Cross-polytope
  • Regular polytope dual to the hypercube in any number of dimensions

    hypercube. The vertex-edge graph of an n-dimensional cross-polytope is the Turán graph T(2n, n) (also known as a cocktail party graph ). In 1 dimension the

    Cross-polytope

    Cross-polytope

    Cross-polytope

  • Conway polyhedron notation
  • Method of describing higher-order polyhedra

    pp. 61–70. Deza, M.; Dutour, M (2004). "Goldberg–Coxeter constructions for 3-and 4-valent plane graphs". The Electronic Journal of Combinatorics. 11: #R20

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • Niemeier lattice
  • Positive-definite integral set of repeated points with Abelian group-rank 24

    rank either 0 or 24, and all of their components have the same Coxeter number. (The Coxeter number, at least in these cases, is the number of roots divided

    Niemeier lattice

    Niemeier_lattice

  • Demihypercube
  • Polytope constructed from alternation of a hypercube

    in the hyperoctahedral group (the Coxeter group B C n {\displaystyle BC_{n}} [4,3n−1]) has index 2. It is the Coxeter group D n , {\displaystyle D_{n}

    Demihypercube

    Demihypercube

    Demihypercube

  • Icosidodecahedron
  • Archimedean solid with 32 faces

    represented as the symmetric graph with 30 vertices and 60 edges, one of the Archimedean graphs. It is a symmetric quartic graph, meaning that each vertex

    Icosidodecahedron

    Icosidodecahedron

    Icosidodecahedron

  • Truncated cuboctahedron
  • Archimedean solid with 26 faces

    cuboctahedron has two special orthogonal projections in the A2 and B2 Coxeter planes with [6] and [8] projective symmetry, and numerous [2] symmetries

    Truncated cuboctahedron

    Truncated cuboctahedron

    Truncated_cuboctahedron

  • Uniform 8-polytope
  • Polytope contained by 7-polytope facets

    permutations of the Coxeter-Dynkin diagrams with one or more rings. See also a list of B8 polytopes for symmetric Coxeter plane graphs of these polytopes

    Uniform 8-polytope

    Uniform 8-polytope

    Uniform_8-polytope

  • Robert Frucht
  • German-Chilean mathematician

    cubic Hamiltonian graphs, was named for the initials of Joshua Lederberg, H. S. M. Coxeter, and Frucht, its key developers.[E] With Coxeter and David L. Powers

    Robert Frucht

    Robert_Frucht

  • The Fifty-Nine Icosahedra
  • Book on stellations of the regular icosahedron by H. S. M. Coxeter and colleagues

    The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie. It enumerates certain stellations

    The Fifty-Nine Icosahedra

    The Fifty-Nine Icosahedra

    The_Fifty-Nine_Icosahedra

  • 57-cell
  • was discovered by H. S. M. Coxeter (1982). The vertices and edges form the Perkel graph, the unique distance-regular graph with intersection array {6

    57-cell

    57-cell

    57-cell

  • List of University of Toronto faculty
  • of Tutte's theorem on perfect matchings, Tutte matrix, Tutte graph, Tutte–Coxeter graph, Tutte 12-cage and Tutte fragment Abraham Robinson (professor

    List of University of Toronto faculty

    List_of_University_of_Toronto_faculty

  • Uniform 10-polytope
  • Type of geometrical object

    symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform

    Uniform 10-polytope

    Uniform 10-polytope

    Uniform_10-polytope

  • Discrete geometry
  • Branch of geometry that studies combinatorial properties and constructive methods

    map colourings by Tait, Heawood, and Hadwiger. László Fejes Tóth, H.S.M. Coxeter, and Paul Erdős laid the foundations of discrete geometry. A polytope is

    Discrete geometry

    Discrete geometry

    Discrete_geometry

  • Exceptional object
  • a set of 12 elements in 2 different ways. The Tutte–Coxeter graph: the symmetries of this graph are the automorphisms of S6. The exceptional automorphism

    Exceptional object

    Exceptional object

    Exceptional_object

  • Truncated cube
  • Archimedean solid with 14 faces

    Publications, Inc. p. 76. ISBN 978-0-486-23729-9. Koca, M.; Koca, N. O. (2013). "Coxeter groups, quaternions, symmetries of polyhedra and 4D polytopes". Mathematical

    Truncated cube

    Truncated cube

    Truncated_cube

  • Stericated 7-simplexes
  • gabach). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by

    Stericated 7-simplexes

    Stericated 7-simplexes

    Stericated_7-simplexes

  • 2 22 honeycomb
  • There are no regular honeycombs in the family since its Coxeter diagram a nonlinear graph, but the 222 and birectified 222 are isotopic, with only one

    2 22 honeycomb

    2_22_honeycomb

AI & ChatGPT searchs for online references containing COXETER GRAPH

COXETER GRAPH

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COXETER GRAPH

  • Marghuba
  • Girl/Female

    Arabic, Muslim

    Marghuba

    Coveted; Desired

    Marghuba

  • Coulter
  • Boy/Male

    English

    Coulter

    young horse;frisky.

    Coulter

  • Cotter
  • Surname or Lastname

    Irish (co. Cork)

    Cotter

    Irish (co. Cork) : reduced Anglicized form of Gaelic Mac Oitir ‘son of Oitir’, a personal name borrowed from Old Norse Óttarr, composed of the elements ótti ‘fear’, ‘dread’ + herr ‘army’.English : status name from Middle English cotter, a technical term in the feudal system for a serf or bond tenant who held a cottage by service rather than rent, from Old English cot ‘cottage’, ‘hut’ (see Coates) + -er agent suffix.Probably an Americanized spelling of German Kotter.

    Cotter

  • Marghub
  • Boy/Male

    Indian

    Marghub

    Desirable, Coveted, Pleasant

    Marghub

  • Marghub |
  • Boy/Male

    Muslim

    Marghub |

    Desirable, Coveted, Pleasant

    Marghub |

  • Marghoob
  • Boy/Male

    Arabic, Muslim

    Marghoob

    Agreeable; Desirable; Coveted

    Marghoob

  • Coulter
  • Boy/Male

    American, Australian, British, English, Irish

    Coulter

    Young Horse; Frisky; Part of a Plough

    Coulter

  • Colter
  • Surname or Lastname

    English

    Colter

    English : occupational name for someone who looked after asses and horses, from an agent derivative of Colt. Compare Coulthard.Variant spelling of German Kolter.

    Colter

  • Kesiraju
  • Boy/Male

    Arabic, Hindu, Indian

    Kesiraju

    Poeter

    Kesiraju

  • Counter
  • Surname or Lastname

    English (Devon)

    Counter

    English (Devon) : occupational name for a treasurer or accountant, from Middle English counter (from Old French conteor).

    Counter

  • Marghuba |
  • Girl/Female

    Muslim

    Marghuba |

    Coveted, Desired

    Marghuba |

  • Marghoob
  • Boy/Male

    Muslim/Islamic

    Marghoob

    Desirable coveted, agreeable

    Marghoob

  • Marghoob
  • Boy/Male

    Indian

    Marghoob

    Desirable, Coveted, Pleasant

    Marghoob

  • Marghoob |
  • Boy/Male

    Muslim

    Marghoob |

    Desirable, Coveted, Pleasant

    Marghoob |

  • Colter
  • Boy/Male

    English American

    Colter

    Horse herdsman. young horse;frisky.

    Colter

  • Exeter
  • Boy/Male

    Shakespearean

    Exeter

    King Henry V' and 'Henry VI, Part 1' and 'King Henry the Sixth, Part III' Duke of Exeter, uncle...

    Exeter

  • Cooter
  • Surname or Lastname

    English (Sussex)

    Cooter

    English (Sussex) : unexplained.

    Cooter

  • Custard
  • Surname or Lastname

    English

    Custard

    English : variant of Coster.

    Custard

  • Colter
  • Boy/Male

    American, British, English

    Colter

    Colt Herder; Keeper of the Colt Herd; Horse Herdsman; Variant of Colt; Young Horse; Frisky

    Colter

  • Coster
  • Surname or Lastname

    English

    Coster

    English : metonymic occupational name for a grower or seller of costards (Anglo-Norman French, from coste ‘rib’), a variety of large apples, so called for their prominent ribs. In some cases, it may have been a nickname (from the same word) for a person with an apple-shaped (i.e. round) head.Dutch : status name for a churchwarden, from Late Latin custor ‘guard’, ‘warden’.Variant spelling of German Koster.This name is recorded in Beverwijck in New Netherland (Albany, NY) in the mid 17th century.

    Coster

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COXETER GRAPH

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COXETER GRAPH

Online names & meanings

  • Aaqil
  • Boy/Male

    Muslim/Islamic

    Aaqil

    Intelligent

  • FLYNN
  • Male

    English

    FLYNN

    Irish surname transferred to forename use, from an Anglicized form of Gaelic Ó Floinn, FLYNN means "descendant of Flann," hence "red, ruddy."

  • Nefin
  • Boy/Male

    German

    Nefin

    Nephew.

  • Hinsley
  • Surname or Lastname

    English

    Hinsley

    English : variant of Hinckley.

  • Severn
  • Boy/Male

    English

    Severn

    Strict. Restrained. Surname.

  • MERTE
  • Female

    Egyptian

    MERTE

    , an uncertain goddess.

  • Succoth
  • Girl/Female

    Biblical

    Succoth

    Tents, tabernacles.

  • Vaageesh
  • Boy/Male

    Hindu, Indian, Malayalam, Marathi

    Vaageesh

    Lord of Speech

  • Konali
  • Girl/Female

    Hindu, Indian

    Konali

    Tender

  • Aksa | அக்ஸா
  • Girl/Female

    Tamil

    Aksa | அக்ஸா

    Soul, Gods blessing, A mosque

AI search & ChatGPT queries for Facebook and twitter users, user names, hashtags with COXETER GRAPH

COXETER GRAPH

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COXETER GRAPH

AI searchs for Acronyms & meanings containing COXETER GRAPH

COXETER GRAPH

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Other words and meanings similar to

COXETER GRAPH

AI search in online dictionary sources & meanings containing COXETER GRAPH

COXETER GRAPH

  • Coveter
  • n.

    One who covets.

  • Countretaille
  • n.

    A counter tally; correspondence (in sound).

  • Counter
  • adv.

    In the wrong way; contrary to the right course; as, a hound that runs counter.

  • Counterrolment
  • n.

    A counter account. See Control.

  • Counter
  • a.

    Contrary; opposite; contrasted; opposed; adverse; antagonistic; as, a counter current; a counter revolution; a counter poison; a counter agent; counter fugue.

  • Coulter
  • n.

    Same as Colter.

  • Counter
  • adv.

    A prefix meaning contrary, opposite, in opposition; as, counteract, counterbalance, countercheck. See Counter, adv. & a.

  • Fish
  • n.

    A counter, used in various games.

  • Culter
  • n.

    A colter. See Colter.

  • Cotter
  • n.

    A piece of wood or metal, commonly wedge-shaped, used for fastening together parts of a machine or structure. It is driven into an opening through one or all of the parts. [See Illust.] In the United States a cotter is commonly called a key.

  • Counterprove
  • v. t.

    To take a counter proof of, or a copy in reverse, by taking an impression directly from the face of an original. See Counter proof, under Counter.

  • Contratenor
  • n.

    Counter tenor; contralto.

  • Cotter
  • v. t.

    To fasten with a cotter.

  • Losenger
  • n.

    A flatterer; a deceiver; a cozener.

  • Covetable
  • a.

    That may be coveted; desirable.

  • Counter
  • adv.

    Same as Contra. Formerly used to designate any under part which served for contrast to a principal part, but now used as equivalent to counter tenor.

  • Compter
  • n.

    A counter.

  • Counterirritation
  • n.

    See Counter irritant, etc., under Counter, a.

  • Control
  • v. t.

    To check by a counter register or duplicate account; to prove by counter statements; to confute.