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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
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
Canadian geometer (1907–2003)
as Coxeter–Dynkin diagram or Coxeter graph. Coxeter denotes these groups and their diagram structures in bracket notations, named as Coxeter notation or
Harold Scott MacDonald Coxeter
Harold_Scott_MacDonald_Coxeter
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
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
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
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
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
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
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
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
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
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
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
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
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
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
symbols (indexed 195−230) in Hermann–Mauguin notation, Fibrifold notation, geometric notation, and Coxeter notation: Conway, John Horton; Delgado Friedrichs
Fibrifold
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
(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
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
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
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
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
product of the Coxeter group symmetry and the fundamental domain symmetry (the Goursat tetrahedron in these cases). Coxeter notation supports this symmetry
Goursat_tetrahedron
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
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
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
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
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
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
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
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Regular tiling of hyperbolic 3-space
subgroup symmetry construction with dodecahedral fundamental domains: Coxeter notation: [4,(3,5)*], index 120. The order-5 cubic honeycomb has a related alternated
Order-5_cubic_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
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
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
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
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)
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
tilings around every edge. In Coxeter notation, the removal of the 3rd and 4th mirrors, [3,6,3*] creates a new Coxeter group [3[3,3]], , subgroup index
Triangular_tiling_honeycomb
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
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
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
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
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)
diagrams. The 10th is constructed as an alternation. As subgroups in Coxeter notation: [3,4,(3,3)*] (index 24), [3,3,4,3*] (index 6), [1+,4,3,3,4,1+] (index
Birectified_16-cell_honeycomb
Number line and triangular tiling's symmetry mathematical structure
n-1} one may identify the Coxeter generator s i {\displaystyle s_{i}} with the affine permutation that has window notation [ 1 , 2 , … , i − 1 , i + 1
Affine_symmetric_group
Graph operation
The Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs
Goldberg–Coxeter_construction
construction contains alternating types, or colors, of tetrahedral cells. In Coxeter notation, this half symmetry is represented as [3,3,6,1+] ↔ [3,((3,3,3))], or
Order-6_tetrahedral_honeycomb
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
Schläfli symbol {6,(3,4,3)}, Coxeter diagram, , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is [6,3,8
Order-3-7_hexagonal_honeycomb
Notation for tesselations
is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter, Longuet-Higgins
Wythoff_symbol
group of the Coxeter–Todd lattice. Coxeter, Finite Groups Generated by Unitary Reflections, 1966, 4. The Graphical Notation, Table of n-dimensional groups
Mitchell's_group
COXETER NOTATION
COXETER NOTATION
Surname or Lastname
English
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.
Surname or Lastname
English (Devon)
English (Devon) : occupational name for a treasurer or accountant, from Middle English counter (from Old French conteor).
Boy/Male
Arabic, Muslim
Agreeable; Desirable; Coveted
Boy/Male
Shakespearean
King Henry V' and 'Henry VI, Part 1' and 'King Henry the Sixth, Part III' Duke of Exeter, uncle...
Girl/Female
Arabic, Muslim
Coveted; Desired
Boy/Male
English American
Horse herdsman. young horse;frisky.
Surname or Lastname
English
English : occupational name for someone who looked after asses and horses, from an agent derivative of Colt. Compare Coulthard.Variant spelling of German Kolter.
Boy/Male
Muslim/Islamic
Desirable coveted, agreeable
Boy/Male
English
young horse;frisky.
Boy/Male
American, British, English
Colt Herder; Keeper of the Colt Herd; Horse Herdsman; Variant of Colt; Young Horse; Frisky
Girl/Female
Muslim
Coveted, Desired
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Surname or Lastname
Irish (co. Cork)
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.
Boy/Male
Indian
Desirable, Coveted, Pleasant
Boy/Male
American, Australian, British, English, Irish
Young Horse; Frisky; Part of a Plough
Surname or Lastname
English (Sussex)
English (Sussex) : unexplained.
Surname or Lastname
English
English : variant of Coster.
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Boy/Male
Arabic, Hindu, Indian
Poeter
Boy/Male
Indian
Desirable, Coveted, Pleasant
COXETER NOTATION
COXETER NOTATION
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Surname or Lastname
English
English : from the Norman personal name Malg(i)er, Maug(i)er, composed of the Germanic elements madal ‘council’ + gÄr, gÄ“er ‘spear’. The surname is now also established in Ulster.Hungarian : from a shortened form of majorosgazda (see Majoros), or a derivative of German Meyer 1.Polish, Czech, and Slovak : from the military rank major (derived from Latin maior ‘greater’), a word related to English mayor and the German surname Meyer.Catalan and southern French (Occitan) : from major ‘major’ (Latin maior ‘greater’), denoting a prominent or important person or the first-born son of a family.Jewish (eastern Ashkenazic) : variant of Meyer 2.
Surname or Lastname
English
English : habitational name from Cavil, a place in the East Riding of Yorkshire, named from Old English cÄ â€˜jackdaw’ + feld ‘open country’.
Surname or Lastname
English
English : possibly a habitational name from Mill Ham, Devon, or Millham Farm in Cornwall and Hereford, or perhaps a variant of Mileham.
Boy/Male
Muslim
Servant of the fashioner (Allah)
Girl/Female
Hebrew American Spanish
Gift from God.
Male
Italian
Italian form of German Berthold, BERTOLDO means "bright ruler."
Girl/Female
Arabic, Australian
Lady of Dignity
Boy/Male
Muslim
Courage
Boy/Male
Indian, Kannada, Tamil
Sweet Like Kuyil (Cuckoo)
COXETER NOTATION
COXETER NOTATION
COXETER NOTATION
COXETER NOTATION
COXETER NOTATION
n.
See Counter irritant, etc., under Counter, a.
n.
A counter account. See Control.
adv.
A prefix meaning contrary, opposite, in opposition; as, counteract, counterbalance, countercheck. See Counter, adv. & a.
n.
A counter.
n.
A counter tally; correspondence (in sound).
n.
A colter. See Colter.
n.
A flatterer; a deceiver; a cozener.
n.
One who covets.
n.
Same as Colter.
n.
A counter, used in various games.
v. t.
To fasten with a cotter.
v. t.
To check by a counter register or duplicate account; to prove by counter statements; to confute.
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.
n.
Counter tenor; contralto.
adv.
In the wrong way; contrary to the right course; as, a hound that runs counter.
a.
Contrary; opposite; contrasted; opposed; adverse; antagonistic; as, a counter current; a counter revolution; a counter poison; a counter agent; counter fugue.
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.
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.
a.
That may be coveted; desirable.