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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds. They were introduced by John Horton Conway, Olaf Delgado Friedrichs,
Fibrifold
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
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
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
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
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
this tiling represents the fundamental domains of [∞,5*] symmetry, orbifold notation *∞∞∞∞∞ symmetry, a pentagonal domain with five ideal vertices. The
Order-5_apeirogonal_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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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-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
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
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
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
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
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
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
ORBIFOLD NOTATION
ORBIFOLD NOTATION
ORBIFOLD NOTATION
ORBIFOLD NOTATION
Girl/Female
Indian
Desire, Aspiration, Desirability
Boy/Male
Muslim
Good attitude, Good manners
Female
Norwegian
Norwegian form of Old Norse ValdÃs, WALDIS means "goddess of the slain in battle."
Boy/Male
Hindu, Indian, Tamil
Lord Krishna
Boy/Male
Hindu, Indian
Victorious; Who Always Win
Girl/Female
Indian
Fruit
Surname or Lastname
English (Lancashire)
English (Lancashire) : unexplained.
Girl/Female
Muslim
Pearl
Girl/Female
Hindu, Indian, Traditional
As Blue as Indra
Girl/Female
Tamil
Coming from Utkal
ORBIFOLD NOTATION
ORBIFOLD NOTATION
ORBIFOLD NOTATION
ORBIFOLD NOTATION
ORBIFOLD NOTATION
n.
The practice of using symbols, or the system of notation developed thereby.
a.
Marked or measured by crotchets; having musical notation.
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.
n.
The written and printed notation of a musical composition; the score.
n.
Literal or etymological signification.
a.
Representing sounds; as, phonetic characters; -- opposed to ideographic; as, a phonetic notation.
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.
n.
A table showing the notation, length, or duration of the several notes.
a.
Twofold; double; of two kinds, degrees, etc.
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.
n.
A character used in musical notation to determine the position and pitch of the scale as represented on the staff.
n.
The act or practice of recording anything by marks, figures, or characters.
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.]
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.
n.
The act of specifying or determining by a mark or limit; notation of limits.
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.
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.
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.
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.
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.