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ORBIFOLD NOTATION

  • Orbifold notation
  • Notation for 2-dimensional spherical, euclidean and hyperbolic symmetry groups

    In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing

    Orbifold notation

    Orbifold_notation

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

    the same wallpaper group; it is called p4m in the IUCr notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4g

    Wallpaper group

    Wallpaper group

    Wallpaper_group

  • 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

  • Conway notation
  • Topics referred to by the same term

    polyhedron notation Conway triangle notation Orbifold notation This disambiguation page lists articles associated with the title Conway notation. If an internal

    Conway notation

    Conway_notation

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

    operator-based approach of Sin-Itiro Tomonaga and Julian Schwinger. The orbifold notation system, invented by William Thurston, has been developed for representing

    History of mathematical notation

    History_of_mathematical_notation

  • Orbifold
  • Generalized manifold

    me. It was obtained by a democratic process in my course of 1976–77. An orbifold is something with many folds; unfortunately, the word "manifold" already

    Orbifold

    Orbifold

    Orbifold

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

    On successive lines are the orbifold notation, the Coxeter notation and Coxeter diagram, and the Hermann–Mauguin notation (full, and abbreviated if different)

    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

  • William Thurston
  • American mathematician (1946–2012)

    Misiurewicz–Thurston points Nielsen–Thurston classification Normal surface Orbifold notation Thurston norm Thurston's 24 questions Thurston's double limit theorem

    William Thurston

    William Thurston

    William_Thurston

  • Icosidodecahedron
  • Archimedean solid with 32 faces

    sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within

    Icosidodecahedron

    Icosidodecahedron

    Icosidodecahedron

  • 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

  • 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

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

    symmetry at the points where the white curves cross. In John Conway's orbifold notation, this set of symmetries is denoted 433. Each fish provides a fundamental

    Circle Limit III

    Circle_Limit_III

  • 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

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

    sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within

    Trihexagonal tiling

    Trihexagonal tiling

    Trihexagonal_tiling

  • 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

  • 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

  • Space group
  • Symmetry group of a configuration in space

    space group + atomic arrangement (motif)). Orbifold notation (2D) Fibrifold notation (3D) Describes the orbifold, given by the quotient of Euclidean space

    Space group

    Space group

    Space_group

  • 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)

  • Orthorhombic crystal system
  • Type of three-dimensional crystal structural geometry

    Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold notation, type, and

    Orthorhombic crystal system

    Orthorhombic_crystal_system

  • 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

  • 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 rotational

    Cyclic symmetry in three dimensions

    Cyclic symmetry in three dimensions

    Cyclic_symmetry_in_three_dimensions

  • 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

  • Disdyakis triacontahedron
  • Catalan solid with 120 faces

    mirrors 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

  • Coxeter notation
  • Classification system for symmetry groups in geometry

    [4+,4] and [6,3+] are semidirect subgroups. Given in Coxeter notation (orbifold notation), some low index affine subgroups are: Rank four groups defined

    Coxeter notation

    Coxeter notation

    Coxeter_notation

  • 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

  • Improper rotation
  • Rotation composed with a reflection

    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 n×,

    Improper rotation

    Improper_rotation

  • 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

  • Regular octahedron
  • Solid with eight equal triangular faces

    sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of ∗ n 32 {\displaystyle ^{*}n32} all of these tilings are

    Regular octahedron

    Regular octahedron

    Regular_octahedron

  • Antiprism
  • Polyhedron with parallel bases connected by triangles

    of the following table, the symbols are Schoenflies, Coxeter, and orbifold notation, in this order. Antiprism graph, graph of an antiprism Grand antiprism

    Antiprism

    Antiprism

    Antiprism

  • Uniform tiling symmetry mutations
  • domains between two symmetry groups. They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean tilings

    Uniform tiling symmetry mutations

    Uniform tiling symmetry mutations

    Uniform_tiling_symmetry_mutations

  • Saccheri quadrilateral
  • Quadrilateral with two equal sides perpendicular to the base

    quadrilaterals have acute summit angles. The tilings exhibit a *nn22 symmetry (orbifold notation), and include: Lambert quadrilateral Boris Abramovich Rozenfelʹd (1988)

    Saccheri quadrilateral

    Saccheri quadrilateral

    Saccheri_quadrilateral

  • Tessellation
  • Covering by shapes without overlaps or gaps

    the seven frieze groups describing the possible frieze patterns. Orbifold notation can be used to describe wallpaper groups of the Euclidean plane. Penrose

    Tessellation

    Tessellation

    Tessellation

  • Skew apeirohedron
  • Infinite polyhedron with non-planar faces

    Larger pattern Space group Related H2 orbifold notation Cubic space group Coxeter notation Fibrifold notation {4,5} 3 cubes Im3m [[4,3,4]] 8°:2 *4222

    Skew apeirohedron

    Skew_apeirohedron

  • Pentagonal tiling
  • Tiling of the plane by pentagons

    unit. The wallpaper group symmetry for each tiling is given, with orbifold notation in parentheses. A second lower symmetry group is given if tile chirality

    Pentagonal tiling

    Pentagonal tiling

    Pentagonal_tiling

  • Bicupola
  • Solid made from 2 cupolae joined base-to-base

    and orbifold notation, in this order. An n-gonal gyrobicupola has the same topology as an n-gonal rectified antiprism, Conway polyhedron notation: aAn

    Bicupola

    Bicupola

  • Hosohedron
  • Spherical polyhedron composed of lunes

    C_{4v}} C 5 v {\displaystyle C_{5v}} C 6 v {\displaystyle C_{6v}} Orbifold notation ( ∗ n n ) {\displaystyle (*nn)} ( ∗ 11 ) {\displaystyle (*11)} ( ∗

    Hosohedron

    Hosohedron

    Hosohedron

  • Truncated tetrahexagonal tiling
  • Semiregular tiling of the hyperbolic plane

    [6*,4]+, subgroup indices 12 and 24 respectively, can be given in orbifold notation as (3333) and (222222). Wikimedia Commons has media related to Uniform

    Truncated tetrahexagonal tiling

    Truncated tetrahexagonal tiling

    Truncated_tetrahexagonal_tiling

  • Rhombitrihexagonal tiling
  • Semiregular tiling of the Euclidean plane

    4): 1232.) With edge-colorings there is a half symmetry form (3*3) orbifold notation. The hexagons can be considered as truncated triangles, t{3} with

    Rhombitrihexagonal tiling

    Rhombitrihexagonal tiling

    Rhombitrihexagonal_tiling

  • Seifert fiber space
  • Topological space

    S 1 {\displaystyle S^{1}} -bundle (circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for all compact

    Seifert fiber space

    Seifert_fiber_space

  • Quarter order-6 square tiling
  • plane. It has Schläfli symbol of q{4,6}. It is constructed from *3232 orbifold notation, and can be seen as a half symmetry of *443 and *662, and quarter

    Quarter order-6 square tiling

    Quarter order-6 square tiling

    Quarter_order-6_square_tiling

  • Truncated trihexagonal tiling
  • Uniform tiling of the Euclidean plane

    tiling triangles represent the fundamental domains of p6m, [6,3] (*632 orbifold notation) wallpaper group symmetry. There are a number of small index subgroups

    Truncated trihexagonal tiling

    Truncated trihexagonal tiling

    Truncated_trihexagonal_tiling

  • Tetrakis square tiling
  • There are many small index subgroups of p4m, [4,4] symmetry (*442 orbifold notation), that can be seen in relation to the Coxeter diagram, with nodes

    Tetrakis square tiling

    Tetrakis square tiling

    Tetrakis_square_tiling

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

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

    Uniform tilings in hyperbolic plane

    Uniform_tilings_in_hyperbolic_plane

  • Non-Euclidean crystallographic group
  • hyperbolic triangle groups are notable NEC groups. Others are listed in Orbifold notation. Non-Euclidean geometry Isometry group Fuchsian group Uniform tilings

    Non-Euclidean crystallographic group

    Non-Euclidean_crystallographic_group

  • Triclinic crystal system
  • One of the seven crystal systems

    examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold, type, and space

    Triclinic crystal system

    Triclinic crystal system

    Triclinic_crystal_system

  • Elongated triangular tiling
  • Semiregular tiling of the plane

    series of symmetry mutations with hyperbolic uniform tilings with 2*n2 orbifold notation symmetry, vertex figure 4.n.4.3.3.3, and Coxeter diagram . Their duals

    Elongated triangular tiling

    Elongated triangular tiling

    Elongated_triangular_tiling

  • Rhombitetraoctagonal tiling
  • Regular tiling of the hyperbolic plane

    right angles. With edge-colorings there is a half symmetry form (4*4) orbifold notation. The octagons can be considered as truncated squares, t{4} with two

    Rhombitetraoctagonal tiling

    Rhombitetraoctagonal tiling

    Rhombitetraoctagonal_tiling

  • Fibrifold
  • fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds. They were introduced by John Horton Conway, Olaf Delgado Friedrichs,

    Fibrifold

    Fibrifold

  • Order-4 apeirogonal tiling
  • Regular tiling in geometry

    This tiling shows the mirror lines of the symmetry group written in orbifold notation as *2∞. Its dual tiling corresponds to the fundamental domains of

    Order-4 apeirogonal tiling

    Order-4 apeirogonal tiling

    Order-4_apeirogonal_tiling

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

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

    Order-4 octagonal tiling

    Order-4 octagonal tiling

    Order-4_octagonal_tiling

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

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

    Order-4 hexagonal tiling

    Order-4 hexagonal tiling

    Order-4_hexagonal_tiling

  • 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

    Order-4 heptagonal tiling

    Order-4 heptagonal tiling

    Order-4_heptagonal_tiling

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

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

    Order-6 square tiling

    Order-6 square tiling

    Order-6_square_tiling

  • Order-5 apeirogonal tiling
  • this tiling represents the fundamental domains of [∞,5*] symmetry, orbifold notation *∞∞∞∞∞ symmetry, a pentagonal domain with five ideal vertices. The

    Order-5 apeirogonal tiling

    Order-5 apeirogonal tiling

    Order-5_apeirogonal_tiling

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

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

    Order-6 hexagonal tiling

    Order-6 hexagonal tiling

    Order-6_hexagonal_tiling

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

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

    Order-4 pentagonal tiling

    Order-4 pentagonal tiling

    Order-4_pentagonal_tiling

  • List of space groups
  • dimensions, given by a number index, and a full name in Hermann–Mauguin notation, and a short name (international short symbol). The long names are given

    List of space groups

    List_of_space_groups

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

    fundamental domain, and 5 mirrors meeting at a point. This symmetry by orbifold notation is called *33333 with 5 order-3 mirror intersections. This tiling

    Order-6 pentagonal tiling

    Order-6 pentagonal tiling

    Order-6_pentagonal_tiling

  • Crystallographic point group
  • Classification system for crystals

    correspondence of the two systems below, see crystal system. In Schoenflies notation, point groups are denoted by a letter symbol with a subscript. The symbols

    Crystallographic point group

    Crystallographic_point_group

  • Rhombitrioctagonal tiling
  • Semiregular tiling of the hyperbolic plane

    rhombitrihexagonal tiling, by edge-coloring there is a half symmetry form (3*4) orbifold notation. The octagons can be considered as truncated squares, t{4} with two

    Rhombitrioctagonal tiling

    Rhombitrioctagonal tiling

    Rhombitrioctagonal_tiling

  • Point groups in four dimensions
  • plane symmetry with two sets of parallel mirrors and a rectangular domain (orbifold *2222). Subgroups include: [p+,2,q], (), [p,2,q+], (), [p+,2,q+], (). And

    Point groups in four dimensions

    Point groups in four dimensions

    Point_groups_in_four_dimensions

  • Rhombitriapeirogonal tiling
  • rhombitrihexagonal tiling, by edge-coloring there is a half symmetry form (3*∞) orbifold notation. The apeireogons can be considered as truncated, t{∞} with two types

    Rhombitriapeirogonal tiling

    Rhombitriapeirogonal tiling

    Rhombitriapeirogonal_tiling

  • Order-6 apeirogonal tiling
  • Tiling of the hyperbolic plane

    this tiling represents the fundamental domains of [∞,6*] symmetry, orbifold notation *∞∞∞∞∞∞ symmetry, a hexagonal domain with five ideal vertices. The

    Order-6 apeirogonal tiling

    Order-6 apeirogonal tiling

    Order-6_apeirogonal_tiling

  • Truncated tetraapeirogonal tiling
  • Concept in mathematics

    [∞*,4]+, subgroup indices 16 and ∞ respectively, can be given in orbifold notation as (∞∞∞∞) and (2∞). Wikimedia Commons has media related to Uniform

    Truncated tetraapeirogonal tiling

    Truncated tetraapeirogonal tiling

    Truncated_tetraapeirogonal_tiling

  • 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

  • Truncated tetraoctagonal tiling
  • Semiregular tiling in geometry

    [8*,4]+, subgroup indices 16 and 32 respectively, can be given in orbifold notation as (4444) and (22222222). From a Wythoff construction there are fourteen

    Truncated tetraoctagonal tiling

    Truncated tetraoctagonal tiling

    Truncated_tetraoctagonal_tiling

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

    and is represented by a Coxeter–Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram, with markup symbols for

    Point group

    Point group

    Point_group

  • Birkhoff–Grothendieck theorem
  • Classifies holomorphic vector bundles over the complex projective line

    It also holds for P 1 {\displaystyle \mathbb {P} ^{1}} with one or two orbifold points, and for chains of projective lines meeting along nodes. One application

    Birkhoff–Grothendieck theorem

    Birkhoff–Grothendieck_theorem

  • Supergravity
  • Modern theory of gravitation that combines supersymmetry and general relativity

    near singularities did not begin to be understood until the advent of orbifold conformal field theories in the late 1980s. Supergravity models generically

    Supergravity

    Supergravity

    Supergravity

  • Line group
  • listed in Hermann-Mauguin notation, and for the point groups, Schönflies notation. There appears to be no comparable notation for the line groups. These

    Line group

    Line_group

  • Manifold
  • Topological space that locally resembles Euclidean space

    infinite-dimensional manifolds are studied in functional analysis. Orbifolds An orbifold is a generalization of manifold allowing for certain kinds of "singularities"

    Manifold

    Manifold

    Manifold

  • The Symmetries of Things
  • 2016 book by John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss

    colored objects, the symmetries of topological spaces described in terms of orbifolds, and abstract forms of symmetry described by group theory and presentations

    The Symmetries of Things

    The_Symmetries_of_Things

  • Non-linear sigma model
  • Class of quantum field theory models

    section of the jet bundle of T×M and V is the potential. In the coordinate notation, with the coordinates Σa, a = 1, ..., n where n is the dimension of T,

    Non-linear sigma model

    Non-linear_sigma_model

  • Point groups in two dimensions
  • Geometry concept

    the rotations in the group. Intl refers to Hermann–Mauguin notation or international notation, often used in crystallography. In the infinite limit, these

    Point groups in two dimensions

    Point groups in two dimensions

    Point_groups_in_two_dimensions

  • Ginzburg–Landau theory
  • Superconductivity theory

    duality was given by relating the Gromov–Witten theory of Calabi–Yau orbifolds to FJRW theory an analogous Landau–Ginzburg "FJRW" theory. Witten's sigma

    Ginzburg–Landau theory

    Ginzburg–Landau_theory

  • Cuboctahedron
  • Polyhedron with 8 triangles and 6 squares

    24 edges can be seen in 4 central hexagons. With octahedral symmetry (orbifold 432), the squares have the 4-fold symmetry, triangles the 3-fold symmetry

    Cuboctahedron

    Cuboctahedron

    Cuboctahedron

  • E8 (mathematics)
  • 248-dimensional exceptional simple Lie group

    groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation

    E8 (mathematics)

    E8 (mathematics)

    E8_(mathematics)

  • Critical three-state Potts model
  • Two dimensional conformal field theory

    tetracritical Ising model by applying a Z 2 {\displaystyle \mathbb {Z} _{2}} orbifold transformation to the latter. The critical three-state Potts conformal

    Critical three-state Potts model

    Critical_three-state_Potts_model

  • E7 (mathematics)
  • 133-dimensional exceptional simple Lie group

    groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation

    E7 (mathematics)

    E7 (mathematics)

    E7_(mathematics)

  • Dichromatic symmetry
  • Two-colour symmetry (examples, history and dimensional counts)

    colour-preserving symmetries of coloured objects using a new notation based on Orbifolds The table below gives the number of ordinary and dichromatic

    Dichromatic symmetry

    Dichromatic symmetry

    Dichromatic_symmetry

  • E6 (mathematics)
  • 78-dimensional exceptional simple Lie group

    {\displaystyle {\mathfrak {e}}_{6}} , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation

    E6 (mathematics)

    E6 (mathematics)

    E6_(mathematics)

  • Superspace
  • Base space for supersymmetric theories

    super Poincaré algebra modulo the algebra of the Lorentz group. A typical notation for the coordinates on such a space is ( x , θ , θ ¯ ) {\displaystyle (x

    Superspace

    Superspace

  • Differential geometry of surfaces
  • Mathematics of smooth surfaces

    freely on S2, so the corresponding quotients are not 2-manifolds, just orbifolds. Non-Euclidean geometry was first discussed in letters of Gauss, who made

    Differential geometry of surfaces

    Differential geometry of surfaces

    Differential_geometry_of_surfaces

  • History of group theory
  • History of a branch of mathematics

    geometry came together to produce exciting new fields. Work on knot theory, orbifolds, hyperbolic manifolds, and groups acting on trees (the Bass–Serre theory)

    History of group theory

    History_of_group_theory

  • AdS/CFT correspondence
  • Duality between theories of gravity on anti-de Sitter space and conformal field theories

    gravitational theory lives is effectively five-dimensional (hence the notation AdS5), and there are five additional compact dimensions (encoded by the

    AdS/CFT correspondence

    AdS/CFT_correspondence

  • Nambu–Goto action
  • Invariant action in bosonic string theory

    b )   {\displaystyle g=\mathrm {det} \left(g_{ab}\right)\ } Using the notation that: X ˙ = ∂ X ∂ τ {\displaystyle {\dot {X}}={\frac {\partial X}{\partial

    Nambu–Goto action

    Nambu–Goto_action

  • Crystal system
  • Classification of crystalline materials by their three-dimensional structural geometry

    Crystal system Point group / Crystal class Schönflies Hermann–Mauguin Orbifold Coxeter Point symmetry Order Abstract group triclinic pedial C1 1 11 [ ]+

    Crystal system

    Crystal system

    Crystal_system

  • Differentiable manifold
  • Manifold upon which it is possible to perform calculus

    use a different notion of chart known as a "plot". Frölicher spaces and orbifolds are other attempts. A rectifiable set generalizes the idea of a piece-wise

    Differentiable manifold

    Differentiable manifold

    Differentiable_manifold

  • Wilson loop
  • Gauge field loop operator

    separations are determined by the Wilson lines. Wilson lines also play a role in orbifold compactifications where their presence leads to greater control of gauge

    Wilson loop

    Wilson_loop

  • Timeline of manifolds
  • Mathematics timeline

    manifolds. There are also related classes, such as homology manifolds and orbifolds, that resemble manifolds. It took a generation for clarity to emerge,

    Timeline of manifolds

    Timeline_of_manifolds

  • Vertex operator algebra
  • Algebra used in 2D conformal field theories and string theory

    called twisted sectors, and are intimately connected with string theory on orbifolds. The lattice vertex algebra construction was the original motivation for

    Vertex operator algebra

    Vertex_operator_algebra

  • Uniform tiling
  • Vertex-transitive tiling of the plane by regular polygons

    has a polygonal fundamental domain and can be represented by its group notation: the sequence of the reflection orders of the fundamental domain vertices

    Uniform tiling

    Uniform_tiling

  • Polychromatic symmetry
  • Symmetry with three or more colours

    colour-preserving symmetries of coloured objects using a new notation based on Orbifolds. Both of the 3-colour p3 patterns, the unique 4-, 6-, 7-colour

    Polychromatic symmetry

    Polychromatic symmetry

    Polychromatic_symmetry

  • Glossary of algebraic geometry
  • structure sheaf O X | U {\displaystyle {\mathcal {O}}_{X}|_{U}} . orbifold Nowadays an orbifold is often defined as a Deligne–Mumford stack over the category

    Glossary of algebraic geometry

    Glossary_of_algebraic_geometry

  • M-theory
  • Framework of superstring theory

    of the gravitational theory is effectively seven-dimensional (hence the notation AdS7), and there are four additional "compact" dimensions (encoded by the

    M-theory

    M-theory

  • Lie groupoid
  • Internal groupoid in the category of smooth manifolds

    smooth manifolds are smooth stacks. Other classes of examples include orbifolds, which are (equivalence classes of) proper étale Lie groupoids, and orbit

    Lie groupoid

    Lie_groupoid

  • Instanton
  • Solitons in Euclidean spacetime

    expression agrees with the well known result of Bender and Wu. In their notation ℏ = 1 , q 0 = 2 K + 1 , h 6 / 2 c 2 = ϵ . {\displaystyle \hbar =1,q_{0}=2K+1

    Instanton

    Instanton

    Instanton

  • Wess–Zumino–Witten model
  • Type of 2D conformal field theory

    = L i e ( G ) {\displaystyle {\mathfrak {g}}=\mathrm {Lie} (G)} , the notation for the affine Lie algebra is g ^ k {\displaystyle {\hat {\mathfrak {g}}}_{k}}

    Wess–Zumino–Witten model

    Wess–Zumino–Witten_model

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Online names & meanings

  • Abilashini
  • Girl/Female

    Indian

    Abilashini

    Desire, Aspiration, Desirability

  • Jazel |
  • Boy/Male

    Muslim

    Jazel |

    Good attitude, Good manners

  • WALDIS
  • Female

    Norwegian

    WALDIS

    Norwegian form of Old Norse Valdís, WALDIS means "goddess of the slain in battle."

  • Madhusudhan
  • Boy/Male

    Hindu, Indian, Tamil

    Madhusudhan

    Lord Krishna

  • Jithvar
  • Boy/Male

    Hindu, Indian

    Jithvar

    Victorious; Who Always Win

  • Hejal
  • Girl/Female

    Indian

    Hejal

    Fruit

  • Crewdson
  • Surname or Lastname

    English (Lancashire)

    Crewdson

    English (Lancashire) : unexplained.

  • Lulua |
  • Girl/Female

    Muslim

    Lulua |

    Pearl

  • Indranilika
  • Girl/Female

    Hindu, Indian, Traditional

    Indranilika

    As Blue as Indra

  • Utkala | உத்கலா
  • Girl/Female

    Tamil

    Utkala | உத்கலா

    Coming from Utkal

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Other words and meanings similar to

ORBIFOLD NOTATION

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ORBIFOLD NOTATION

  • Symbolism
  • n.

    The practice of using symbols, or the system of notation developed thereby.

  • Crotcheted
  • a.

    Marked or measured by crotchets; having musical notation.

  • Fluxion
  • n.

    A method of analysis developed by Newton, and based on the conception of all magnitudes as generated by motion, and involving in their changes the notion of velocity or rate of change. Its results are the same as those of the differential and integral calculus, from which it differs little except in notation and logical method.

  • Music
  • n.

    The written and printed notation of a musical composition; the score.

  • Notation
  • n.

    Literal or etymological signification.

  • Phonetic
  • a.

    Representing sounds; as, phonetic characters; -- opposed to ideographic; as, a phonetic notation.

  • Quadrillion
  • n.

    According to the French notation, which is followed also upon the Continent and in the United States, a unit with fifteen ciphers annexed; according to the English notation, the number produced by involving a million to the fourth power, or the number represented by a unit with twenty-four ciphers annexed. See the Note under Numeration.

  • Time-table
  • n.

    A table showing the notation, length, or duration of the several notes.

  • Bifold
  • a.

    Twofold; double; of two kinds, degrees, etc.

  • Trillion
  • n.

    According to the French notation, which is used upon the Continent generally and in the United States, the number expressed by a unit with twelve ciphers annexed; a million millions; according to the English notation, the number produced by involving a million to the third power, or the number represented by a unit with eighteen ciphers annexed. See the Note under Numeration.

  • Clef
  • n.

    A character used in musical notation to determine the position and pitch of the scale as represented on the staff.

  • Notation
  • n.

    The act or practice of recording anything by marks, figures, or characters.

  • Decillion
  • n.

    According to the English notation, a million involved to the tenth power, or a unit with sixty ciphers annexed; according to the French and American notation, a thousand involved to the eleventh power, or a unit with thirty-three ciphers annexed. [See the Note under Numeration.]

  • Notation
  • n.

    Any particular system of characters, symbols, or abbreviated expressions used in art or science, to express briefly technical facts, quantities, etc. Esp., the system of figures, letters, and signs used in arithmetic and algebra to express number, quantity, or operations.

  • Specification
  • n.

    The act of specifying or determining by a mark or limit; notation of limits.

  • Decimal
  • a.

    Of or pertaining to decimals; numbered or proceeding by tens; having a tenfold increase or decrease, each unit being ten times the unit next smaller; as, decimal notation; a decimal coinage.

  • Nonillion
  • n.

    According to the French and American notation, a thousand octillions, or a unit with thirty ciphers annexed; according to the English notation, a million octillions, or a unit with fifty-four ciphers annexed. See the Note under Numeration.

  • Quintilllion
  • n.

    According to the French notation, which is used on the Continent and in America, the cube of a million, or a unit with eighteen ciphers annexed; according to the English notation, a number produced by involving a million to the fifth power, or a unit with thirty ciphers annexed. See the Note under Numeration.

  • Grace
  • n.

    Ornamental notes or short passages, either introduced by the performer, or indicated by the composer, in which case the notation signs are called grace notes, appeggiaturas, turns, etc.

  • Romic
  • n.

    A method of notation for all spoken sounds, proposed by Mr. Sweet; -- so called because it is based on the common Roman-letter alphabet. It is like the palaeotype of Mr. Ellis in the general plan, but simpler.