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COXETER COMPLEX

  • Coxeter complex
  • Simplicial complex

    the Coxeter complex, named after H. S. M. Coxeter, is a geometrical structure (a simplicial complex) associated to a Coxeter group. Coxeter complexes are

    Coxeter complex

    Coxeter_complex

  • 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

  • Building (mathematics)
  • Mathematical structure

    a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W, S), called the Coxeter complex. A building Δ is glued

    Building (mathematics)

    Building_(mathematics)

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

    In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic

    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

  • Regular 4-polytope
  • Four-dimensional analogues of the regular polyhedra in three dimensions

    Coxeter 1973, § 1.8 Configurations Coxeter, Complex Regular Polytopes, p. 117 Conway, Burgiel & Goodman-Strauss 2008, p. 406, Fig 26.2 Coxeter, Star

    Regular 4-polytope

    Regular 4-polytope

    Regular_4-polytope

  • Complex polytope
  • Generalization of a polytope in real space

    symbolic notation developed by Coxeter. Some complex polytopes which are not fully regular have also been described. The complex line C 1 {\displaystyle \mathbb

    Complex polytope

    Complex_polytope

  • Complex reflection group
  • Concept in mathematics

    real reflection groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra). A (complex) reflection r (sometimes also

    Complex reflection group

    Complex_reflection_group

  • Ordered Bell number
  • Number of orderings allowing ties

    number of faces in the Coxeter complex associated with a Coxeter group of type A n − 1 {\displaystyle A_{n-1}} . Here, a Coxeter group can be thought of

    Ordered Bell number

    Ordered Bell number

    Ordered_Bell_number

  • Regular complex polygon
  • Polygons which have an accompanying imaginary dimension for each real dimension

    regular complex polygons have been completely characterized, and can be described using a symbolic notation developed by Coxeter. A regular complex polygon

    Regular complex polygon

    Regular complex polygon

    Regular_complex_polygon

  • Tesseract
  • Four-dimensional analogue of the cube

    1007/s11075-022-01278-y. Coxeter 1973, p. 12, §1.8 Configurations. Coxeter 1973, p. 293. Coxeter, H. S. M., Regular Complex Polytopes, second edition

    Tesseract

    Tesseract

    Tesseract

  • 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

  • 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

  • Weyl distance function
  • the Coxeter complexes that make them up are colorable. A coloring of a building is associated with a uniform choice of Weyl group for the Coxeter complexes

    Weyl distance function

    Weyl_distance_function

  • Boerdijk–Coxeter helix
  • Linear stacking of regular tetrahedra that form helices

    The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and Arie Hendrick Boerdijk [es], is a linear stacking of regular tetrahedra, arranged so that

    Boerdijk–Coxeter helix

    Boerdijk–Coxeter helix

    Boerdijk–Coxeter_helix

  • Shelling (topology)
  • Mathematical concept

    previous property. Every Coxeter complex, and more generally every building (in the sense of Tits), is shellable. The boundary complex of a (convex) polytope

    Shelling (topology)

    Shelling_(topology)

  • Parabolic subgroup of a reflection group
  • Mathematical group

    complex reflection group, so the complex reflection groups form another generalization of finite real reflection groups. Suppose that W is a Coxeter group

    Parabolic subgroup of a reflection group

    Parabolic_subgroup_of_a_reflection_group

  • Hessian polyhedron
  • quasiregular form. Coxeter, Complex Regular polytopes, p.123 Coxeter Regular Convex Polytopes, 12.5 The Witting polytope Coxeter, Complex Regular polytopes

    Hessian polyhedron

    Hessian polyhedron

    Hessian_polyhedron

  • Dynkin diagram
  • Pictorial representation of symmetry

    Dynkin diagrams exactly coincide with Coxeter diagrams, as there are no multiple edges. Dynkin diagrams classify complex semisimple Lie algebras. Real semisimple

    Dynkin diagram

    Dynkin diagram

    Dynkin_diagram

  • Isomorphism problem of Coxeter groups
  • dimensional, locally finite, ranked simplicial complex to capture isomorphisms between finite rank Coxeter systems) and asked more related open questions

    Isomorphism problem of Coxeter groups

    Isomorphism_problem_of_Coxeter_groups

  • 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

  • 1 22 polytope
  • Uniform 6-polytope

    polytopes, named as V72 (for its 72 vertices). Its Coxeter symbol is 122, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end

    1 22 polytope

    1 22 polytope

    1_22_polytope

  • Complex geometry
  • Study of complex manifolds and several complex variables

    complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry

    Complex geometry

    Complex_geometry

  • Binary tetrahedral group
  • Nonabelian group in algebraic group theory

    subgroup of Spin(3) of order 24. The complex reflection group named 3(24)3 by G.C. Shephard or 3[3]3 and by Coxeter, is isomorphic to the binary tetrahedral

    Binary tetrahedral group

    Binary tetrahedral group

    Binary_tetrahedral_group

  • Witting polytope
  • In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices

    Witting polytope

    Witting polytope

    Witting_polytope

  • Projective geometry
  • Type of geometry

    1997, p. 88. Coxeter 2003, p. v. Coxeter 1969, p. 229. Coxeter 2003, p. 14. Coxeter 1969, pp. 93, 261. Coxeter 1969, pp. 234–238. Coxeter 2003, pp. 111–132

    Projective geometry

    Projective_geometry

  • Iwahori–Hecke algebra
  • Deformation of the group algebra of a Coxeter group

    of the group algebra of a Coxeter group. The Hecke algebra can also be viewed as a q-analog of the group algebra of a Coxeter group. Hecke algebras are

    Iwahori–Hecke algebra

    Iwahori–Hecke_algebra

  • Möbius–Kantor polygon
  • Every vertex is shared by 3 triangular edges. Coxeter named it a Möbius–Kantor polygon for sharing the complex configuration structure as the Möbius–Kantor

    Möbius–Kantor polygon

    Möbius–Kantor polygon

    Möbius–Kantor_polygon

  • Goldberg–Coxeter construction
  • Graph operation

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

    Goldberg–Coxeter construction

    Goldberg–Coxeter construction

    Goldberg–Coxeter_construction

  • Complex polygon
  • Polygon in complex space, or which self-intersects

    meshes:Surface (polygonal) Simplification 1997. (retrieved May 2016) Coxeter, H. S. M., Regular Complex Polytopes, Cambridge University Press, 1974. Introduction

    Complex polygon

    Complex_polygon

  • 5-cube
  • 5-dimensional hypercube

    polytopes in n dimensions (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    5-cube

    5-cube

  • 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

  • M. C. Escher
  • Dutch graphic artist (1898–1972)

    interacted with the mathematicians George Pólya, Roger Penrose, and Donald Coxeter, and the crystallographer Friedrich Haag, and conducted his own research

    M. C. Escher

    M. C. Escher

    M._C._Escher

  • Pentellated 7-cubes
  • gotesa) 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

    Pentellated 7-cubes

    Pentellated 7-cubes

    Pentellated_7-cubes

  • Weyl group
  • Subgroup of a root system's isometry group

    reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semisimple

    Weyl group

    Weyl group

    Weyl_group

  • Four-dimensional space
  • Geometric space with four dimensions

    posthumously in 1901, and remained largely unknown until publication of H.S.M. Coxeter's Regular Polytopes in 1947. During that interval many others also discovered

    Four-dimensional space

    Four-dimensional space

    Four-dimensional_space

  • Great complex icosidodecahedron
  • Degenerate uniform star polyhedron

    hidden, being completely contained inside the first. Small complex icosidodecahedron Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J

    Great complex icosidodecahedron

    Great complex icosidodecahedron

    Great_complex_icosidodecahedron

  • Configuration (polytope)
  • In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.[citation needed] Other configurations in geometry are something

    Configuration (polytope)

    Configuration_(polytope)

  • Reflection group
  • Discrete group type in group theory

    group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the

    Reflection group

    Reflection_group

  • Affine symmetric group
  • Number line and triangular tiling's symmetry mathematical structure

    and certain complex reflection groups. Many of their combinatorial and geometric properties extend to the broader family of affine Coxeter groups. The

    Affine symmetric group

    Affine symmetric group

    Affine_symmetric_group

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

    of 1. The Goldberg-Coxeter (GC) Conway operators are two infinite families of operators that are an extension of the Goldberg-Coxeter construction. The

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • Straightedge and compass construction
  • Method of drawing geometric objects

    us to consider the points as a set of complex numbers. Given any such interpretation of a set of points as complex numbers, the points constructible using

    Straightedge and compass construction

    Straightedge and compass construction

    Straightedge_and_compass_construction

  • Polytope
  • Geometric object with flat sides

    generalised the idea as complex polytopes in complex space, where each real dimension has an imaginary one associated with it. Coxeter developed the theory

    Polytope

    Polytope

  • Mitchell's group
  • Coxeter gives it group symbol [1 2 3]3 and Coxeter-Dynkin diagram . Mitchell's group is an index 2 subgroup of the automorphism group of the Coxeter–Todd

    Mitchell's group

    Mitchell's_group

  • Regular polytope
  • Polytope with highest degree of symmetry

    Coxeter (1973), p. 143. Walter & Deloudi (2009), p. 50. Walter & Deloudi (2009), p. 51. Barnes (2012), p. 46. Coxeter (1973), pp. 120–121. Coxeter (1973)

    Regular polytope

    Regular polytope

    Regular_polytope

  • 3-4 duoprism
  • Duocylinder Tesseract Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, (1974). Regular Polytopes, H. S. M. Coxeter, Dover Publications

    3-4 duoprism

    3-4 duoprism

    3-4_duoprism

  • 7-cube
  • 7-dimensional hypercube

    polytopes in n dimensions (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    7-cube

    7-cube

    7-cube

  • Kazhdan–Lusztig polynomial
  • Integral polynomial

    George Lusztig (1979). They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group. In the

    Kazhdan–Lusztig polynomial

    Kazhdan–Lusztig_polynomial

  • Coxeter–Todd lattice
  • In mathematics, the Coxeter–Todd lattice K12, discovered by Coxeter and Todd (1953), is a 12-dimensional even integral lattice of discriminant 36 with

    Coxeter–Todd lattice

    Coxeter–Todd lattice

    Coxeter–Todd_lattice

  • Hexagonal tiling
  • Regular tiling of a two-dimensional space

    book, Keith Critchlow, pp. 74–75, pattern 2 Coxeter, Regular Complex Polytopes, pp. 111–112, p. 136. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973)

    Hexagonal tiling

    Hexagonal tiling

    Hexagonal_tiling

  • Pentellated 7-orthoplexes
  • gotaz) 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

    Pentellated 7-orthoplexes

    Pentellated 7-orthoplexes

    Pentellated_7-orthoplexes

  • Stericated 7-cubes
  • gabcosaz) 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-cubes

    Stericated 7-cubes

    Stericated_7-cubes

  • Bruhat order
  • Partial order on a Coxeter group

    order, or Chevalley–Bruhat order) is a partial order on the elements of a Coxeter group, that corresponds to the inclusion order on Schubert varieties. The

    Bruhat order

    Bruhat_order

  • 5-orthoplex
  • Convex regular 5-polytope in geometry

     117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes (2nd ed

    5-orthoplex

    5-orthoplex

    5-orthoplex

  • 7-orthoplex
  • Regular 7- polytope

    Regular Polytopes, 3rd edition, Dover, New York, 1973 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    7-orthoplex

    7-orthoplex

    7-orthoplex

  • Skew polygon
  • Polygonal chain whose vertices are not all coplanar

    (Saddle Polygons)" §2.2 Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M.; Regular complex polytopes (1974). Chapter

    Skew polygon

    Skew polygon

    Skew_polygon

  • Algebraic geometry
  • Branch of mathematics

    mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. As a study of systems of polynomial

    Algebraic geometry

    Algebraic geometry

    Algebraic_geometry

  • Bernhard Riemann
  • German mathematician (1826–1866)

    contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis

    Bernhard Riemann

    Bernhard Riemann

    Bernhard_Riemann

  • 600-cell
  • Four-dimensional analog of the icosahedron

    2: 55–65, 110–120 Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed

    600-cell

    600-cell

    600-cell

  • 5-demicube
  • Regular 5-polytope

    Polytopes, three regular polytopes in n dimensions (n ≥ 5) Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes (2nd ed.). Cambridge University Press. ISBN 0-521-39490-2

    5-demicube

    5-demicube

    5-demicube

  • Compound of five cubes
  • Polyhedral compound

    The 30 rhombic faces exist in the planes of the 5 cubes. Coxeter 1973, pp. 49-50. Coxeter 1973, p 98. Cromwell (1997), pp. 360–361. Cromwell, Peter R

    Compound of five cubes

    Compound of five cubes

    Compound_of_five_cubes

  • Affine geometry
  • Euclidean geometry without distance and angles

    118 (exercise 3). Coxeter 1955, The Affine Plane, § 2: Affine geometry as an independent system Coxeter 1955, Affine plane, p. 8 Coxeter, Introduction to

    Affine geometry

    Affine geometry

    Affine_geometry

  • Trihexagonal tiling
  • Tiling of a plane by regular hexagons and equilateral triangles

    Dimensional symmetry Mutations". CiteSeerX 10.1.1.30.8536. Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed.). Cambridge University Press. pp. 111–2

    Trihexagonal tiling

    Trihexagonal tiling

    Trihexagonal_tiling

  • 24-cell
  • Regular object in four dimensional geometry

    (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991), Regular Complex Polytopes (2nd ed.), Cambridge: Cambridge University Press Coxeter, H.S.M. (1995), Sherk

    24-cell

    24-cell

    24-cell

  • 7-demicube
  • Uniform 7-polytope

    polytopes in n dimensions (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    7-demicube

    7-demicube

    7-demicube

  • Eight-dimensional space
  • Geometric space with eight dimensions

    of reflection, each domain defined by a Coxeter group. Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram. The 8-demicube is a unique

    Eight-dimensional space

    Eight-dimensional_space

  • Stericated 7-orthoplexes
  • gocaz) 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-orthoplexes

    Stericated 7-orthoplexes

    Stericated_7-orthoplexes

  • Small complex icosidodecahedron
  • vertices, similarly to how its 3D equivalent shares edges. Great complex icosidodecahedron Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J

    Small complex icosidodecahedron

    Small complex icosidodecahedron

    Small_complex_icosidodecahedron

  • Hypercube
  • Convex polytope, the n-dimensional analogue of a square and a cube

    (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The hypercube is the special

    Hypercube

    Hypercube

    Hypercube

  • 6-orthoplex
  • Regular 6 dimensional polytope

    crystal H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge

    6-orthoplex

    6-orthoplex

    6-orthoplex

  • 2 21 polytope
  • Uniform 6-polytope

    It is also called the Schläfli polytope. Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end

    2 21 polytope

    2 21 polytope

    2_21_polytope

  • 6-cube
  • 6-dimensional hypercube

    polytopes in n dimensions (n ≥ 5). ISBN 0-486-61480-8. Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    6-cube

    6-cube

    6-cube

  • Polygon
  • Plane figure bounded by line segments

    the center of the image, Coxeter, H.S.M.; Regular Polytopes, 3rd Edn, Dover (pbk), 1973, p. 114 Shephard, G.C.; "Regular complex polytopes", Proc. London

    Polygon

    Polygon

  • 6-demicube
  • Uniform 6-polytope

    [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2. Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    6-demicube

    6-demicube

    6-demicube

  • Outline of geometry
  • Overview of and topical guide to geometry

    Sphericon Stereographic projection Stereometry Ball Convex Convex hull Coxeter group Euclidean distance Homothetic center Hyperplane Lattice Ehrhart polynomial

    Outline of geometry

    Outline_of_geometry

  • Mirrors and Reflections
  • Undergraduate mathematics textbook

    dihedral groups, and root systems. Part III of the book concerns Coxeter complexes, and uses them as the basis for some group theory of reflection groups

    Mirrors and Reflections

    Mirrors_and_Reflections

  • 8-cube
  • 8-dimensional hypercube

    Polytopes, three regular polytopes in n dimensions (n ≥ 5) Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    8-cube

    8-cube

    8-cube

  • 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

  • J. A. Todd
  • British geometer

    in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice. In 1954 he and G. C. Shephard classified the finite complex reflection groups. In March

    J. A. Todd

    J._A._Todd

  • LCF notation
  • Representation of cubic graphs

    code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain

    LCF notation

    LCF notation

    LCF_notation

  • Two-dimensional space
  • Mathematical space with two coordinates

    two-dimensional complex space – such as the two-dimensional complex coordinate space, the complex projective plane, or a complex surface – has two complex dimensions

    Two-dimensional space

    Two-dimensional_space

  • Perpendicular
  • Relationship between two lines that meet at a right angle

    Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana

    Perpendicular

    Perpendicular

    Perpendicular

  • John Flinders Petrie
  • Developer of the Petrie polygon

    navigator, Matthew Flinders. He met the geometer Harold Scott MacDonald Coxeter as a student, beginning a lifelong friendship. They collaborated in discovering

    John Flinders Petrie

    John_Flinders_Petrie

  • List of regular polytopes
  • Honeycombs, p. 224. ISBN 978-1-107-10340-5. Coxeter (1973), p. 120. Coxeter (1973), p. 124. Coxeter, Regular Complex Polytopes, p. 9 Duncan, Hugh (28 September

    List of regular polytopes

    List of regular polytopes

    List_of_regular_polytopes

  • Cyclohedron
  • Polytope associated with combinatorial problems

    doi:10.4153/CMB-2002-054-1. Carr, Michael; Devadoss, Satyan (2006). "Coxeter complexes and graph-associahedra". Topology and Its Applications. 153 (12):

    Cyclohedron

    Cyclohedron

    Cyclohedron

  • 16-cell
  • Four-dimensional analog of the octahedron

    Macmillan, 1900 H.S.M. Coxeter: Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed

    16-cell

    16-cell

    16-cell

  • Simple Lie group
  • Connected non-abelian Lie group lacking nontrivial connected normal subgroups

    group of type B, C, F, or G is simply laced. Cartan matrix Coxeter matrix Weyl group Coxeter group Kac–Moody algebra Catastrophe theory Table of Lie groups

    Simple Lie group

    Simple Lie group

    Simple_Lie_group

  • Hyperoctahedral group
  • Group of symmetries of an n-dimensional hypercube

    of hyperoctahedral groups forms type B in the classification of finite Coxeter groups. The hyperoctahedral groups were named by Alfred Young in 1930.

    Hyperoctahedral group

    Hyperoctahedral group

    Hyperoctahedral_group

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

    (3): 196–200, doi:10.2307/2975549, JSTOR 2975549. Coxeter, Regular Complex Polytopes, p. 108 Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York:

    Cross-polytope

    Cross-polytope

    Cross-polytope

  • Michael W. Davis
  • American mathematician (born 1949)

    Coxeter groups, Artin groups, and buildings. In his book, The Geometry and Topology of Coxeter Groups, he constructs the Davis complexes for Coxeter groups

    Michael W. Davis

    Michael W. Davis

    Michael_W._Davis

  • Artin–Tits group
  • Family of infinite discrete groups

    groups defined by simple presentations. They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and

    Artin–Tits group

    Artin–Tits_group

  • List of polyhedral stellations
  • different stellation methods occurring in the 1900s, principally from Coxeter et al. (1938) and soon afterward, Pawley (1975). A short generalized table

    List of polyhedral stellations

    List_of_polyhedral_stellations

  • Hosohedron
  • Spherical polyhedron composed of lunes

    in English. MAA. pp. 108–109. ISBN 978-0-88385-511-9. Coxeter, H.S.M. (1974). Regular Complex Polytopes. London: Cambridge University Press. p. 20. ISBN 0-521-20125-X

    Hosohedron

    Hosohedron

    Hosohedron

  • Geometry
  • Branch of mathematics

    including Zenodorus. Archimedes, Plato, Euclid, and later Kepler and Coxeter all studied convex polytopes and their properties. From the 19th century

    Geometry

    Geometry

  • Descartes' theorem
  • Equation for radii of tangent circles

    Beecroft and by H. S. M. Coxeter involve four more circles, passing through triples of tangencies of the original three circles; Coxeter also provided a proof

    Descartes' theorem

    Descartes' theorem

    Descartes'_theorem

  • Art Tower Mito
  • Art gallery

    acoustical design by Nagata Acoustics. The design is based on the Boerdijk–Coxeter helix. Wikimedia Commons has media related to Art Tower Mito. Kairakuen

    Art Tower Mito

    Art Tower Mito

    Art_Tower_Mito

  • Line segment
  • Part of a line that is bounded by two distinct end points; line with two endpoints

    Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana

    Line segment

    Line segment

    Line_segment

  • Pythagorean theorem
  • Relation between sides of a right triangle

    Fritz wrote a careful discussion of Hippasus's contributions. For any complex number z = x + i y , {\displaystyle z=x+iy,} the absolute value or modulus

    Pythagorean theorem

    Pythagorean theorem

    Pythagorean_theorem

  • Square tiling
  • Regular tiling of the Euclidean plane

    S2CID 121456259. Grünbaum & Shephard (1987), p. 473–481. Coxeter, Regular Complex Polytopes, pp. 111-112, p. 136. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973)

    Square tiling

    Square tiling

    Square_tiling

  • 8-orthoplex
  • Convex regular 8-polytope

    Regular Polytopes, 3rd edition, Dover, New York, 1973 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2

    8-orthoplex

    8-orthoplex

    8-orthoplex

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  • 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

  • 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

  • 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

  • Colter
  • Boy/Male

    American, British, English

    Colter

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

    Colter

  • Marghub
  • Boy/Male

    Indian

    Marghub

    Desirable, Coveted, Pleasant

    Marghub

  • Coulter
  • Boy/Male

    American, Australian, British, English, Irish

    Coulter

    Young Horse; Frisky; Part of a Plough

    Coulter

  • Marghoob |
  • Boy/Male

    Muslim

    Marghoob |

    Desirable, Coveted, Pleasant

    Marghoob |

  • Marghoob
  • Boy/Male

    Arabic, Muslim

    Marghoob

    Agreeable; Desirable; Coveted

    Marghoob

  • Marghoob
  • Boy/Male

    Muslim/Islamic

    Marghoob

    Desirable coveted, agreeable

    Marghoob

  • Marghoob
  • Boy/Male

    Indian

    Marghoob

    Desirable, Coveted, Pleasant

    Marghoob

  • Cooter
  • Surname or Lastname

    English (Sussex)

    Cooter

    English (Sussex) : unexplained.

    Cooter

  • 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

  • Coulter
  • Boy/Male

    English

    Coulter

    young horse;frisky.

    Coulter

  • Marghuba |
  • Girl/Female

    Muslim

    Marghuba |

    Coveted, Desired

    Marghuba |

  • Kesiraju
  • Boy/Male

    Arabic, Hindu, Indian

    Kesiraju

    Poeter

    Kesiraju

  • 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

  • Marghub |
  • Boy/Male

    Muslim

    Marghub |

    Desirable, Coveted, Pleasant

    Marghub |

  • Custard
  • Surname or Lastname

    English

    Custard

    English : variant of Coster.

    Custard

  • Colter
  • Boy/Male

    English American

    Colter

    Horse herdsman. young horse;frisky.

    Colter

  • Marghuba
  • Girl/Female

    Arabic, Muslim

    Marghuba

    Coveted; Desired

    Marghuba

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Online names & meanings

  • Deuteronomy
  • Biblical

    Deuteronomy

    repetition of the law

  • Birchfield
  • Surname or Lastname

    English

    Birchfield

    English : variant spelling of Burchfield.Americanized form of German Birkenfeld, a topographic or habitational name, cognate with 1.

  • KISHA
  • Female

    English

    KISHA

    Variant spelling of English Keisha, KISHA means "cassia," a bark similar to cinnamon.

  • Jian
  • Boy/Male

    Arabic

    Jian

    Life

  • Galvin
  • Boy/Male

    British, English, Gaelic, Irish

    Galvin

    Sparrow; Brilliantly White

  • Nellie
  • Girl/Female

    American, Australian, British, Christian, Danish, Dutch, English, French, German, Greek, Jamaican, Latin, Swedish

    Nellie

    Shining Light; Eleanor; Most Beautiful Woman; Derived from the Greek Helen; The Bright One; Horn Coloured; Yellow; Form of Cornelius; Horn; Sun Ray; Torch; Moon; Moon Elope; Diminutive of Eleanor; Diminutive of

  • Izaan |
  • Boy/Male

    Muslim

    Izaan |

    Obedience

  • Trusler
  • Surname or Lastname

    English

    Trusler

    English : according to Reaney, this is a variant of Truslow.

  • Anzil | انزیل
  • Boy/Male

    Muslim

    Anzil | انزیل

    Decisive

  • Swarajdeep
  • Boy/Male

    Sikh

    Swarajdeep

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Other words and meanings similar to

COXETER COMPLEX

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  • 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.

  • Counter
  • adv.

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

  • Losenger
  • n.

    A flatterer; a deceiver; a cozener.

  • Coveter
  • n.

    One who covets.

  • 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.

  • Contratenor
  • n.

    Counter tenor; contralto.

  • Cotter
  • v. t.

    To fasten with a cotter.

  • Countretaille
  • n.

    A counter tally; correspondence (in sound).

  • Fish
  • n.

    A counter, used in various games.

  • 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.

  • Control
  • v. t.

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

  • Counter
  • adv.

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

  • 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.

  • Covetable
  • a.

    That may be coveted; desirable.

  • Compter
  • n.

    A counter.

  • Counterrolment
  • n.

    A counter account. See Control.

  • Culter
  • n.

    A colter. See Colter.

  • Counterirritation
  • n.

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