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COXETER NOTATION

  • 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

  • Wallpaper group
  • Classification of a two-dimensional repetitive pattern

    pattern: houndstooth Orbifold signature: *2222 Coxeter notation (rectangular): [∞,2,∞] or [∞]×[∞] Coxeter notation (square): [4,1+,4] or [1+,4,4,1+] Lattice:

    Wallpaper group

    Wallpaper group

    Wallpaper_group

  • Point group
  • Group of geometric symmetries with at least one fixed point

    n Coxeter group has n mirrors and is represented by a Coxeter–Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram

    Point group

    Point group

    Point_group

  • Point groups in four dimensions
  • four-dimensional crystal classes 1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway and Smith

    Point groups in four dimensions

    Point groups in four dimensions

    Point_groups_in_four_dimensions

  • List of planar symmetry groups
  • named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane:

    List of planar symmetry groups

    List_of_planar_symmetry_groups

  • 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

  • Schläfli symbol
  • Notation for polytopes and tessellations

    represented by ( ). Its Coxeter diagram is empty. Its Coxeter notation symmetry is ][. In 1D, a line segment is represented by { }. Its Coxeter diagram is . Its

    Schläfli symbol

    Schläfli symbol

    Schläfli_symbol

  • Point groups in three dimensions
  • Groups of point isometries in 3 dimensions

    planes passing through the same point are the finite Coxeter groups, represented by Coxeter notation. The point groups in three dimensions are widely used

    Point groups in three dimensions

    Point_groups_in_three_dimensions

  • Square lattice
  • 2-dimensional integer lattice

    symmetry groups; its symmetry group in IUC notation as p4m, Coxeter notation as [4,4], and orbifold notation as *442. Two orientations of an image of the

    Square lattice

    Square lattice

    Square_lattice

  • List of spherical symmetry groups
  • groups by Schoenflies notation, Coxeter notation, orbifold notation, and order. John Conway used a variation of the Schoenflies notation, based on the groups'

    List of spherical symmetry groups

    List_of_spherical_symmetry_groups

  • 5-cube
  • 5-dimensional hypercube

    reflection. The Schläfli symbol for the 5-cube, {4,3,3,3}, matches the Coxeter notation symmetry [4,3,3,3]. All hypercubes have lower symmetry forms constructed

    5-cube

    5-cube

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

    In geometry and topology, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • History of mathematical notation
  • Origin and evolution of the symbols used to write equations and formulas

    the Conway chained arrow notation, the Conway notation of knot theory, and the Conway polyhedron notation. The Coxeter notation system classifies symmetry

    History of mathematical notation

    History_of_mathematical_notation

  • Skew apeirohedron
  • Infinite polyhedron with non-planar faces

    solid the figure is sometimes called a partial honeycomb. According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons

    Skew apeirohedron

    Skew_apeirohedron

  • LCF notation
  • Representation of cubic graphs

    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, for the

    LCF notation

    LCF notation

    LCF_notation

  • Triangular prismatic honeycomb
  • (1995). Kaleidoscopes: Selected Writings of H.S.M. Coxeter. Wiley. ISBN 978-0-471-01003-6. Paper 22: Coxeter, H.S.M. (1940). "Regular and Semi-Regular Polytopes

    Triangular prismatic honeycomb

    Triangular prismatic honeycomb

    Triangular_prismatic_honeycomb

  • Icosahedral symmetry
  • 3D symmetry group

    The full symmetry group is the Coxeter group of type H3. It may be represented by Coxeter notation [5,3] and Coxeter diagram . The set of rotational

    Icosahedral symmetry

    Icosahedral symmetry

    Icosahedral_symmetry

  • Cyclic symmetry in three dimensions
  • vertical axis of symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation. Chiral Cn, [n]+, (nn) of order n - n-fold

    Cyclic symmetry in three dimensions

    Cyclic symmetry in three dimensions

    Cyclic_symmetry_in_three_dimensions

  • Dihedral symmetry in three dimensions
  • Regular polygonal symmetry

    three dimensions, each shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation. Chiral Dn, [n,2]+, (22n) of order 2n –

    Dihedral symmetry in three dimensions

    Dihedral_symmetry_in_three_dimensions

  • 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

  • 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

  • Hexagonal lattice
  • One of the five 2D Bravais lattices

    hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the

    Hexagonal lattice

    Hexagonal lattice

    Hexagonal_lattice

  • Mathematical notation
  • System of symbolic representation

    mathematical notations are mostly diagrammatic, and so are almost entirely script independent. Examples are Penrose graphical notation and Coxeter–Dynkin diagrams

    Mathematical notation

    Mathematical notation

    Mathematical_notation

  • Disdyakis triacontahedron
  • Catalan solid with 120 faces

    at each triangle face vertex. This is *n32 in orbifold notation, and [n,3] in Coxeter notation. Conway, Symmetries of things, p.284 "DisdyakisTriacontahedron"

    Disdyakis triacontahedron

    Disdyakis triacontahedron

    Disdyakis_triacontahedron

  • Order-infinite-3 triangular honeycomb
  • symbol {3,∞1,1}, Coxeter diagram, , with alternating types or colors of infinite-order triangular tiling cells. In Coxeter notation the half symmetry

    Order-infinite-3 triangular honeycomb

    Order-infinite-3_triangular_honeycomb

  • Monoclinic crystal system
  • One of the 7 crystal systems in crystallography

    Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for

    Monoclinic crystal system

    Monoclinic crystal system

    Monoclinic_crystal_system

  • Oblique lattice
  • 2-dimensional inclined lattice

    oblique lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the

    Oblique lattice

    Oblique lattice

    Oblique_lattice

  • Graphic notation
  • Topics referred to by the same term

    (dance) A diagrammatic notation in mathematical notation In physics: Penrose graphical notation Coxeter–Dynkin diagram A visual programming language in

    Graphic notation

    Graphic_notation

  • Fibrifold
  • symbols (indexed 195−230) in Hermann–Mauguin notation, Fibrifold notation, geometric notation, and Coxeter notation: Conway, John Horton; Delgado Friedrichs

    Fibrifold

    Fibrifold

  • Uniform 5-polytope
  • Five-dimensional geometric shape

    truncation indexing notation, but require an explicit numbering system on the nodes for clarity. There are five fundamental affine Coxeter groups, and 13 prismatic

    Uniform 5-polytope

    Uniform 5-polytope

    Uniform_5-polytope

  • Space group
  • Symmetry group of a configuration in space

    needed] Coxeter notation Spatial and point symmetry groups, represented as modifications of the pure reflectional Coxeter groups. Geometric notation A geometric

    Space group

    Space group

    Space_group

  • Glide reflection
  • Geometric transformation combining reflection and translation

    translation. It can also be given a Schoenflies notation as S2∞, Coxeter notation as [∞+,2+], and orbifold notation as ∞×. In the Euclidean plane, reflections

    Glide reflection

    Glide reflection

    Glide_reflection

  • Tetragonal crystal system
  • Lattice point group

    by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples. There is only one tetragonal

    Tetragonal crystal system

    Tetragonal crystal system

    Tetragonal_crystal_system

  • Cube
  • Solid with six equal square faces

    \mathrm {R} /\ell } , Coxeter's notation for the circumradius, midradius, and inradius, respectively, also noting that Coxeter uses 2 ℓ {\displaystyle

    Cube

    Cube

    Cube

  • Order-4 hexagonal tiling
  • Regular tiling of the hyperbolic plane

    domain. This symmetry by orbifold notation is called *222222 with 6 order-2 mirror intersections. In Coxeter notation can be represented as [6*,4], removing

    Order-4 hexagonal tiling

    Order-4 hexagonal tiling

    Order-4_hexagonal_tiling

  • Octahedral symmetry
  • 3D symmetry group

    needed for octahedral symmetry, which represent the three mirrors of a Coxeter–Dynkin diagram. The product of the reflections produce 3 rotational generators

    Octahedral symmetry

    Octahedral symmetry

    Octahedral_symmetry

  • Regular dodecahedron
  • Solid with 12 equal pentagonal faces

    \mathrm {R} /\ell } , Coxeter's notation for the circumradius, midradius, and inradius, respectively, also noting that Coxeter uses 2 ℓ {\displaystyle

    Regular dodecahedron

    Regular dodecahedron

    Regular_dodecahedron

  • Uniform honeycombs in hyperbolic space
  • Tiling of hyperbolic 3-space by uniform polyhedra

    uniform polyhedral cells. In 3-dimensional hyperbolic space there are nine Coxeter group families of compact convex uniform honeycombs, generated as Wythoff

    Uniform honeycombs in hyperbolic space

    Uniform honeycombs in hyperbolic space

    Uniform_honeycombs_in_hyperbolic_space

  • Order-7-3 triangular honeycomb
  • Schläfli symbol {3,71,1}, Coxeter diagram, , with alternating types or colors of order-7 triangular tiling cells. In Coxeter notation the half symmetry is

    Order-7-3 triangular honeycomb

    Order-7-3_triangular_honeycomb

  • Bitruncated cubic honeycomb
  • Space-filling tessellation

    {\tilde {A}}_{3}} Coxeter group. This honeycomb has four uniform constructions, with the truncated octahedral cells having different Coxeter groups and Wythoff

    Bitruncated cubic honeycomb

    Bitruncated cubic honeycomb

    Bitruncated_cubic_honeycomb

  • Order-7 tetrahedral honeycomb
  • Schläfli symbol {3,(3,4,3)}, Coxeter diagram, , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is [3,3,8

    Order-7 tetrahedral honeycomb

    Order-7_tetrahedral_honeycomb

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

    {\displaystyle k<n/2} . Some authors use the notation G P G ( n , k ) {\displaystyle GPG(n,k)} . Coxeter's notation for the same graph would be { n } + { n

    Generalized Petersen graph

    Generalized Petersen graph

    Generalized_Petersen_graph

  • Frieze group
  • Type of symmetry group

    in the table below using Hermann–Mauguin notation, Coxeter notation, Schönflies notation, orbifold notation, nicknames created by mathematician John H

    Frieze group

    Frieze group

    Frieze_group

  • E8 lattice
  • Lattice in 8-dimensional space with special properties

    dimensions as degenerate n+1 polytopes). In Coxeter's notation, Gosset's honeycomb is denoted by 521 and has the Coxeter-Dynkin diagram: This honeycomb is highly

    E8 lattice

    E8_lattice

  • Order-4 pentagonal tiling
  • Regular tiling of the hyperbolic plane

    pentagon. This symmetry by orbifold notation is called *22222 with 5 order-2 mirror intersections. In Coxeter notation can be represented as [5*,4], removing

    Order-4 pentagonal tiling

    Order-4 pentagonal tiling

    Order-4_pentagonal_tiling

  • Tetrahedral bipyramid
  • Four-dimensional shape

    tetrahedral prism, , so it can also be given a Coxeter-Dynkin diagram, , and both have Coxeter notation symmetry [2,3,3], order 48. Being convex with all

    Tetrahedral bipyramid

    Tetrahedral bipyramid

    Tetrahedral_bipyramid

  • Regular icosahedron
  • Solid with twenty equal triangular faces

    1 R {\displaystyle {}_{1}\!\mathrm {R} } is Coxeter's notation for the midradius, also noting that Coxeter uses 2 ℓ {\displaystyle 2\ell } as the edge

    Regular icosahedron

    Regular icosahedron

    Regular_icosahedron

  • 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

  • Improper rotation
  • Rotation composed with a reflection

    The Coxeter notation for S2n is [2n+,2+] and , as an index 4 subgroup of [2n,2], , generated as the product of 3 reflections. The Orbifold notation is

    Improper rotation

    Improper_rotation

  • Cubic crystal system
  • Crystallographic system where the unit cell is in the shape of a cube

    class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, international tables for

    Cubic crystal system

    Cubic crystal system

    Cubic_crystal_system

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

    hyperoctahedrons which are analogous to the octahedron in three dimensions. It is Coxeter's β 4 {\displaystyle \beta _{4}} polytope. The dual polytope is the tesseract

    16-cell

    16-cell

    16-cell

  • Lattice (group)
  • Periodic set of points

    lattice Λ {\displaystyle \Lambda } is given in IUCr notation, Orbifold notation, and Coxeter notation, along with a wallpaper diagram showing the symmetry

    Lattice (group)

    Lattice (group)

    Lattice_(group)

  • Rectangular lattice
  • 2-dimensional lattice

    rectangular lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the

    Rectangular lattice

    Rectangular lattice

    Rectangular_lattice

  • Triangular prism
  • Prism with a 3-sided base

    (equilateral triangles and squares in the case of the triangular prism). In Coxeter's notation the triangular prism is given the symbol −121. The triangular prism

    Triangular prism

    Triangular prism

    Triangular_prism

  • Tetrahedral-octahedral honeycomb
  • Quasiregular space-filling tesselation

    This scaliform honeycomb is represented by Coxeter diagram , and symbol s3{2,4,4}, with coxeter notation symmetry [2+,4,4]. . The runcicantic cubic honeycomb

    Tetrahedral-octahedral honeycomb

    Tetrahedral-octahedral honeycomb

    Tetrahedral-octahedral_honeycomb

  • List of regular polytope compounds
  • form k{n/m}, as 2{5/2}, rather than the commonly used {10/4}. Coxeter's extended notation for compounds is of the form c{m,n,...}[d{p,q,...}]e{s,t,...}

    List of regular polytope compounds

    List_of_regular_polytope_compounds

  • 5-demicube
  • Regular 5-polytope

    5-demicube). In Coxeter's notation the 5-demicube is given the symbol 121. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter (1991), p. 117.

    5-demicube

    5-demicube

    5-demicube

  • Tetragonal disphenoid honeycomb
  • honeycomb Coxeter–Dynkin diagrams Cell Isosceles square pyramid Faces Triangle square Space group Fibrifold notation Pm3m (221) 4−:2 Coxeter group C ~

    Tetragonal disphenoid honeycomb

    Tetragonal disphenoid honeycomb

    Tetragonal_disphenoid_honeycomb

  • Cantellation (geometry)
  • Geometric operation on a regular polytope

    birectified form. Chamfer (geometry) Conway polyhedron notation Uniform 4-polytope Uniform polyhedron Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973),

    Cantellation (geometry)

    Cantellation (geometry)

    Cantellation_(geometry)

  • Uniform tilings in hyperbolic plane
  • Symmetric subdivision in hyperbolic geometry

    also exist in the hyperbolic plane, with the *3222 orbifold ([∞,3,∞] Coxeter notation) as the smallest family. There are 9 generation locations for uniform

    Uniform tilings in hyperbolic plane

    Uniform_tilings_in_hyperbolic_plane

  • Snub (geometry)
  • Geometric operation applied to a polyhedron

    Conway polyhedron notation, which can be applied to polyhedra and tilings. Conway calls Coxeter's operation a semi-snub. In this notation, snub is defined

    Snub (geometry)

    Snub (geometry)

    Snub_(geometry)

  • Order-6 square tiling
  • Regular tiling of the hyperbolic plane

    vertex. This symmetry by orbifold notation is called (*3333) with 4 order-3 mirror intersections. In Coxeter notation can be represented as [6,4*], removing

    Order-6 square tiling

    Order-6 square tiling

    Order-6_square_tiling

  • Order-6-4 triangular honeycomb
  • Schläfli symbol {3,61,1}, Coxeter diagram, , with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is [3,6

    Order-6-4 triangular honeycomb

    Order-6-4_triangular_honeycomb

  • Complex polytope
  • Generalization of a polytope in real space

    completely characterized, and can be described using a symbolic notation developed by Coxeter. Some complex polytopes which are not fully regular have also

    Complex polytope

    Complex_polytope

  • Snub rhombicuboctahedron
  • called the Conway snub cuboctahedron in but will be confused with the Coxeter snub cuboctahedron, the snub cube. See snub cuboctahedron. The snub rhombicuboctahedron

    Snub rhombicuboctahedron

    Snub rhombicuboctahedron

    Snub_rhombicuboctahedron

  • Tetrakis square tiling
  • subgroups of p4m, [4,4] symmetry (*442 orbifold notation), that can be seen in relation to the Coxeter diagram, with nodes colored to correspond to reflection

    Tetrakis square tiling

    Tetrakis square tiling

    Tetrakis_square_tiling

  • Goursat tetrahedron
  • product of the Coxeter group symmetry and the fundamental domain symmetry (the Goursat tetrahedron in these cases). Coxeter notation supports this symmetry

    Goursat tetrahedron

    Goursat tetrahedron

    Goursat_tetrahedron

  • Architectonic and catoptric tessellation
  • Uniform Euclidean 3D tessellations and their duals

    Johnson (11-19, 21-25, 31-34, 41-49, 51-52, 61-65), and Grünbaum(1-28). Coxeters names are based on δ4 as a cubic honeycomb, hδ4 as an alternated cubic

    Architectonic and catoptric tessellation

    Architectonic and catoptric tessellation

    Architectonic_and_catoptric_tessellation

  • Order-4 octagonal tiling
  • Regular tiling of the hyperbolic plane

    This symmetry by orbifold notation is called (*22222222) or (*28) with 8 order-2 mirror intersections. In Coxeter notation can be represented as [8*,4]

    Order-4 octagonal tiling

    Order-4 octagonal tiling

    Order-4_octagonal_tiling

  • Order-8-3 triangular honeycomb
  • Schläfli symbol {3,81,1}, Coxeter diagram, , with alternating types or colors of order-8 triangular tiling cells. In Coxeter notation the half symmetry is

    Order-8-3 triangular honeycomb

    Order-8-3_triangular_honeycomb

  • Order-5 octahedral honeycomb
  • Tesselation in regular space

    Schläfli symbol {3,(4,3,4)}, Coxeter diagram, , with alternating types or colors of octahedral cells. In Coxeter notation the half symmetry is [3,4,6,1+]

    Order-5 octahedral honeycomb

    Order-5_octahedral_honeycomb

  • Regular octahedron
  • Solid with eight equal triangular faces

    \mathrm {R} /\ell } , Coxeter's notation for the circumradius, midradius, and inradius, respectively, also noting that Coxeter uses 2 ℓ {\displaystyle

    Regular octahedron

    Regular octahedron

    Regular_octahedron

  • Order-4-5 square honeycomb
  • Schläfli symbol {4,(4,3,4)}, Coxeter diagram, , with alternating types or colors of square tiling cells. In Coxeter notation the half symmetry is [4,4,6

    Order-4-5 square honeycomb

    Order-4-5_square_honeycomb

  • Gosset–Elte figures
  • Group of irregular uniform polytopes

    In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated

    Gosset–Elte figures

    Gosset–Elte figures

    Gosset–Elte_figures

  • Geodesic polyhedron
  • Polyhedron made from triangles that approximates a sphere

    (which is a regular dodecahedron) have mostly hexagonal faces. The Goldberg–Coxeter construction is an expansion of the concepts underlying geodesic polyhedra

    Geodesic polyhedron

    Geodesic polyhedron

    Geodesic_polyhedron

  • Order-6 hexagonal tiling
  • Regular tiling of the hyperbolic plane

    domain. This symmetry by orbifold notation is called *333333 with 6 order-3 mirror intersections. In Coxeter notation can be represented as [6*,6], removing

    Order-6 hexagonal tiling

    Order-6 hexagonal tiling

    Order-6_hexagonal_tiling

  • Italo Jose Dejter
  • Argentine-born American mathematician

    of Coxeter notation (7,3)8. The dual graph of Γ' in T3 is the distance-regular Klein quartic graph, with corresponding dual map of Coxeter notation (3

    Italo Jose Dejter

    Italo Jose Dejter

    Italo_Jose_Dejter

  • Dynkin diagram
  • Pictorial representation of symmetry

    Coxeter group, a specific isomorphism depends on an ordered choice of simple roots. Likewise, while Dynkin diagram notation is standardized, Coxeter diagram

    Dynkin diagram

    Dynkin diagram

    Dynkin_diagram

  • Polyhedral group
  • Geometric polyhedral group

    × reflection, order 2 Wythoff symbol List of spherical symmetry groups Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973. (The Polyhedral

    Polyhedral group

    Polyhedral_group

  • Order-4 heptagonal tiling
  • Regular tiling of the hyperbolic plane

    heptagon. This symmetry by orbifold notation is called *2222222 with 7 order-2 mirror intersections. In Coxeter notation can be represented as [1+,7,1+,4]

    Order-4 heptagonal tiling

    Order-4 heptagonal tiling

    Order-4_heptagonal_tiling

  • 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

  • Line group
  • resulting line group is called a rod group. There are 75 rod groups. The Coxeter notation is based on the rectangular wallpaper groups, with the vertical axis

    Line group

    Line_group

  • A4 polytope
  • with Conway quaternion notation +1/60[I×I].21. Its abstract structure is the symmetric group S5. Three forms with symmetric Coxeter diagrams have extended

    A4 polytope

    A4 polytope

    A4_polytope

  • Uniform polytope
  • Isogonal polytope with uniform facets

    fundamental region of the object. An extension of Schläfli notation, also used by Coxeter, applies to all dimensions; it consists of the letter 't', followed

    Uniform polytope

    Uniform polytope

    Uniform_polytope

  • Order-3-7 heptagonal honeycomb
  • Regular space-filling tessellation with Schläfli symbol (7,3,7)

    honeycomb, Schläfli symbol {8,(3,4,3)}, Coxeter diagram, , with alternating types or colors of cells. In Coxeter notation the half symmetry is [8,3,8,1+] =

    Order-3-7 heptagonal honeycomb

    Order-3-7_heptagonal_honeycomb

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

    completely characterized, and can be described using a symbolic notation developed by Coxeter. A regular complex polygon with all 2-edges can be represented

    Regular complex polygon

    Regular complex polygon

    Regular_complex_polygon

  • 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

  • Permutation
  • Mathematical version of an order change

    symmetric groups. This graded partial order often appears in the context of Coxeter groups. One way to represent permutations of n things is by an integer

    Permutation

    Permutation

    Permutation

  • Polytope compound
  • 3D shape made of polyhedra sharing a common center

    polyhedral compounds can also be regarded as dual-regular compounds. Coxeter's notation for regular compounds is given in the table above, incorporating Schläfli

    Polytope compound

    Polytope_compound

  • Order-4 icosahedral honeycomb
  • Schläfli symbol {3,51,1}, Coxeter diagram, , with alternating types or colors of icosahedral cells. In Coxeter notation the half symmetry is [3,5,4

    Order-4 icosahedral honeycomb

    Order-4_icosahedral_honeycomb

  • Hexagonal tiling honeycomb
  • Regular paracompact honeycomb

    4, 6, 12 and 24 times larger fundamental domains respectively. In Coxeter notation subgroup markups, they are related as: [6,(3,3)*] (remove 3 mirrors

    Hexagonal tiling honeycomb

    Hexagonal tiling honeycomb

    Hexagonal_tiling_honeycomb

  • Icosahedral bipyramid
  • 4-D polytope; direct sum of an icosahedron and a segment

    dual of a dodecahedral prism, Coxeter-Dynkin diagram , so the bipyramid can be described as . Both have Coxeter notation symmetry [2,3,5], order 240. Having

    Icosahedral bipyramid

    Icosahedral bipyramid

    Icosahedral_bipyramid

  • Rectification (geometry)
  • Operation in Euclidean geometry

    4-polytope Uniform polyhedron Weisstein, Eric W. "Rectification". MathWorld. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

    Rectification (geometry)

    Rectification (geometry)

    Rectification_(geometry)

  • Perspective (geometry)
  • Term in geometry

    Mathematical Association of America, ISBN 0-88385-522-4 . 21,2. Coxeter 1969, p. 233 exercise 2 Coxeter, Harold Scott MacDonald (1969), Introduction to Geometry

    Perspective (geometry)

    Perspective (geometry)

    Perspective_(geometry)

  • 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

  • Uniform 6-polytope
  • Uniform 6-dimensional polytope

    construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected

    Uniform 6-polytope

    Uniform 6-polytope

    Uniform_6-polytope

  • Circle Limit III
  • 1959 woodcut by M. C. Escher

    from Escher to H. S. M. Coxeter, Escher wrote that he was inspired to make his Circle Limit series by a figure in Coxeter's article "Crystal Symmetry

    Circle Limit III

    Circle_Limit_III

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

    size 2. The Coxeter–Dynkin diagram for S n ± {\displaystyle S_{n}^{\pm }} is ... with n nodes; the corresponding Coxeter bracket notation is [3, 3, 3

    Hyperoctahedral group

    Hyperoctahedral group

    Hyperoctahedral_group

  • 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

  • Midsphere
  • Sphere tangent to every edge of a polyhedron

    {R} } is Coxeter's notation for the midradius, noting also that Coxeter uses 2 ℓ {\displaystyle 2\ell } as the edge length (see p. 2). Coxeter (1973) states

    Midsphere

    Midsphere

    Midsphere

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COXETER NOTATION

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COXETER NOTATION

  • Marghub |
  • Boy/Male

    Muslim

    Marghub |

    Desirable, Coveted, Pleasant

    Marghub |

  • 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

  • Colter
  • Boy/Male

    American, British, English

    Colter

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

    Colter

  • Marghoob
  • Boy/Male

    Arabic, Muslim

    Marghoob

    Agreeable; Desirable; Coveted

    Marghoob

  • Marghuba |
  • Girl/Female

    Muslim

    Marghuba |

    Coveted, Desired

    Marghuba |

  • 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

  • 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

  • Marghoob |
  • Boy/Male

    Muslim

    Marghoob |

    Desirable, Coveted, Pleasant

    Marghoob |

  • 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

  • Marghoob
  • Boy/Male

    Indian

    Marghoob

    Desirable, Coveted, Pleasant

    Marghoob

  • Coulter
  • Boy/Male

    English

    Coulter

    young horse;frisky.

    Coulter

  • Kesiraju
  • Boy/Male

    Arabic, Hindu, Indian

    Kesiraju

    Poeter

    Kesiraju

  • 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

  • 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

  • Marghoob
  • Boy/Male

    Muslim/Islamic

    Marghoob

    Desirable coveted, agreeable

    Marghoob

  • Colter
  • Boy/Male

    English American

    Colter

    Horse herdsman. young horse;frisky.

    Colter

  • Marghuba
  • Girl/Female

    Arabic, Muslim

    Marghuba

    Coveted; Desired

    Marghuba

  • Cooter
  • Surname or Lastname

    English (Sussex)

    Cooter

    English (Sussex) : unexplained.

    Cooter

  • Custard
  • Surname or Lastname

    English

    Custard

    English : variant of Coster.

    Custard

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Online names & meanings

  • Milagros
  • Girl/Female

    American, Australian, Spanish

    Milagros

    Miracle

  • Satyayu
  • Boy/Male

    Hindu, Indian

    Satyayu

    It's a Truthful and Pious Life

  • Vidwan
  • Boy/Male

    Hindu, Indian

    Vidwan

    Wisdom; Knowledge

  • Sinchana
  • Girl/Female

    Hindu

    Sinchana

    Spurthi

  • Srinivas | ஷ்ரீநிவாஸ
  • Boy/Male

    Tamil

    Srinivas | ஷ்ரீநிவாஸ

    Lord Venkateshwara, Residence of Goddess of wealth, Abode of wealth

  • Thatch
  • Surname or Lastname

    English

    Thatch

    English : perhaps from a metonymic occupational name for a Thatcher, or a nickname for someone with thick blond hair.

  • Drewes
  • Surname or Lastname

    English and Scottish

    Drewes

    English and Scottish : patronymic from the personal name Drew.Danish, Dutch, and German : from a vernacular form of the personal name Andreas.

  • Fairless
  • Surname or Lastname

    English (Northumberland)

    Fairless

    English (Northumberland) : said to be a variant of Scottish Fairlie.

  • Nazneen
  • Girl/Female

    Muslim/Islamic

    Nazneen

    Beautiful

  • Dericka
  • Girl/Female

    English

    Dericka

    Gifted ruler. Modern feminine of Derek.

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Other words and meanings similar to

COXETER NOTATION

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COXETER NOTATION

  • 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.

  • Culter
  • n.

    A colter. See Colter.

  • Coveter
  • n.

    One who covets.

  • Losenger
  • n.

    A flatterer; a deceiver; a cozener.

  • Contratenor
  • n.

    Counter tenor; contralto.

  • 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.

  • 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.

  • Fish
  • n.

    A counter, used in various games.

  • Counterirritation
  • n.

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

  • Compter
  • n.

    A counter.

  • Cotter
  • v. t.

    To fasten with a cotter.

  • 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.

  • Counter
  • a.

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

  • Counterrolment
  • n.

    A counter account. See Control.

  • Coulter
  • n.

    Same as Colter.

  • Countretaille
  • n.

    A counter tally; correspondence (in sound).

  • Covetable
  • a.

    That may be coveted; desirable.

  • Counter
  • adv.

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