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Discrete group type in group theory
In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space
Reflection_group
Concept in mathematics
a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial
Complex_reflection_group
Geometric symmetry operation
point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among
Point_reflection
Group that admits a formal description in terms of reflections
Coxeter groups are precisely the finite Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter group. However
Coxeter_group
Group of geometric symmetries with at least one fixed point
or it is a reflection or improper rotation (determinant of M = −1). The geometric symmetries of crystals are described by space groups, which allow
Point_group
Group of symmetries of a regular polygon
mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest
Dihedral_group
Mathematical group
the mathematical theory of reflection groups, the parabolic subgroups are a special kind of subgroup. In the symmetric group of permutations of the set
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Mapping from a Euclidean space to itself
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of
Reflection_(mathematics)
Isometry of the Eluclidean plane
translations, rotations, reflections, and glide reflections (see below § Classification). The set of Euclidean plane isometries forms a group under composition:
Euclidean_plane_isometry
Subgroup of a root system's isometry group
finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semisimple
Weyl_group
Pictorial representation of symmetry
symmetry group of a regular complex polygon is not called a Coxeter group, but instead a Shephard group, a type of Complex reflection group. The order
Coxeter–Dynkin_diagram
Group of symmetries of an n-dimensional hypercube
two-element group generated by the point reflection through the origin. If one divides the cube into chambers by the planes fixed by each of its reflection symmetries
Hyperoctahedral_group
Invariance under a mathematical reflection
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure
Reflection_symmetry
Number line and triangular tiling's symmetry mathematical structure
symmetric groups have close relationships with other mathematical objects, including juggling patterns and certain complex reflection groups. Many of their
Affine_symmetric_group
In mathematics, Mitchell's group is a complex reflection group in 6 complex dimensions of order 108 × 9!, introduced by Mitchell (1914). It has the structure
Mitchell's_group
Political party in São Tomé and Príncipe
The Democratic Convergence Party-Reflection Group (Portuguese: Partido de Convergência Democrática-Grupo de Reflexão), or PCD-GR, is a political party
Democratic Convergence Party (São Tomé and Príncipe)
Democratic_Convergence_Party_(São_Tomé_and_Príncipe)
Geometric transformation combining reflection and translation
space groups (which describe e.g. crystal symmetries). Objects with glide-reflection symmetry are in general not symmetrical under reflection alone,
Glide_reflection
Set with associative invertible operation
two group elements the same if they differ by an element of a given subgroup. For example, in the symmetry group of a square, once any reflection is performed
Group_(mathematics)
fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular
Vinberg's_algorithm
Classification of a two-dimensional repetitive pattern
wallpaper group of A and B is different from the wallpaper group of C. Another transformation is a glide reflection, a combination of reflection and translation
Wallpaper_group
named for Alfred Young. When S n {\displaystyle S_{n}} is viewed as a reflection group, its Young subgroups are precisely its parabolic subgroups. They may
Young_subgroup
Type of group in abstract algebra
the first nonabelian symmetric group. This group is isomorphic to the dihedral group of order 6, the group of reflection and rotation symmetries of an
Symmetric_group
European intergovernmental advisory group
The E-Infrastructure Reflection Group (e-IRG) is a European inter-governmental advisory group dealing with policies on electronic infrastructures (e-Infrastructures)
E-Infrastructure Reflection Group
E-Infrastructure_Reflection_Group
Type of symmetry group
and reflection in the horizontal axis (isomorphic to C2, the cyclic group of order 2). the groups each consisting of the identity and reflection in a
Frieze_group
Pictorial representation of symmetry
algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. Various properties of the Dynkin
Dynkin_diagram
Group of symmetries of the square
other two, the dihedral group of order 8 and the quaternion group, are not. The action of a rotation or diagonal reflection on the corners of a square
Dihedral_group_of_order_8
Non-commutative group with 6 elements
one with a 3-fold rotation axis in a plane of reflection (and hence also in two other planes of reflection): C3v Consider three colored blocks (red, green
Dihedral_group_of_order_6
Symmetry group in 1D systems
group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent
One-dimensional symmetry group
One-dimensional_symmetry_group
Group realized geometrically by reflections across the sides of a triangle
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle
Triangle_group
Concept in algebraic topology
difference that the Weyl group, rather than being a finite reflection group over the integers, is now a finite p-adic reflection group. They admit a classification
P-compact_group
The reflection group is a hyperbolic reflection group acting on 25-dimensional hyperbolic space. The fundamental domain of the reflection group has 1+23+284
II25,1
Isometry group of Euclidean space
inhomogeneous special orthogonal group. The Euclidean group E(n) comprises all translations, rotations, and reflections of E n {\displaystyle \mathbb {E} ^{n}} ;
Euclidean_group
Topics referred to by the same term
Reflection map may refer to: Reflection mapping in computer graphics A reflection (mathematics), specifically an element of a reflection group an element
Reflection_map
Vertex algebra acted on by the monster group
torus induced by the Leech lattice and orbifolded by the two-element reflection group. Borcherds, Richard (1986), "Vertex algebras, Kac-Moody algebras, and
Monster_vertex_algebra
Solstice-class cruise ship
Celebrity Reflection is the fifth, final, and largest Solstice-class cruise ship, her sister ships being Celebrity Equinox, Celebrity Eclipse, Celebrity
Celebrity_Reflection
group is a complex reflection group, 3[3]3[3]3 or of order 648, and the product of this with a group of order 2 is another complex reflection group,
Hessian_group
Type of mathematical group
dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along an axis. Every dihedral group is generated
Infinite_dihedral_group
Geometry concept
subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations
Point groups in two dimensions
Point_groups_in_two_dimensions
Undergraduate mathematics textbook
Mirrors and Reflections: The Geometry of Finite Reflection Groups is an undergraduate-level textbook on the geometry of reflection groups. It was written
Mirrors_and_Reflections
Groups of point isometries in 3 dimensions
its full symmetry group if and only if the object is chiral. The point groups that are generated purely by a finite set of reflection mirror planes passing
Point groups in three dimensions
Point_groups_in_three_dimensions
Australian mathematician
Robert Howlett), and the determination of the action of a complex reflection group on the cohomology of the complement of its reflecting hyperplanes.
Gustav_Lehrer
Mathematical abelian group
as the symmetry group of a non-square rectangle (with the three non-identity elements being horizontal reflection, vertical reflection and 180-degree rotation)
Klein_four-group
Spherical triangle that can be used to tile a sphere
angle, the orientation-preserving subgroup of the reflection group of the triangle is a Hecke group. For an ideal triangle in which all angles are zero
Schwarz_triangle
Day of Reflection group considers how best the conflict can be collectively remembered and reflected upon. The first Day of Private Reflection took place
Healing_Through_Remembering
Capacity of humans to exercise introspection
Self-reflection is the ability to witness and evaluate one's own cognitive, emotional, and behavioural processes. In psychology, other terms used for this
Self-reflection
hyperbolic reflection group), but rather to the ordinary triangle group (the von Dyck group) D(2,3,7) of orientation-preserving maps (the rotation group), which
(2,3,7)_triangle_group
of Reflection was specifically mentioned by the report of the Consultative Group on the Past who recommended that it be renamed the Day of Reflection and
Day_of_Private_Reflection
plane symmetry groups: Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through
Plane_symmetry
Nonabelian group in algebraic group theory
by the spin group. It follows that the binary tetrahedral group is a discrete subgroup of Spin(3) of order 24. The complex reflection group named 3(24)3
Binary_tetrahedral_group
Digital infrastructure promoting data sharing
within collections, archives, and databases. The e-Infrastructure Reflection Group (e-IRG) has proposed a similar vision. In particular, it envisions
Data_infrastructure
Reflected duplication of an object
and mathematics they form the principal objects of Coxeter group theory and reflection groups. In chemistry, two versions (isomers) of a molecule, one a
Mirror_image
6th President of Latvia
pro-European, as such, in December 2007 she was named vice-chair of the Reflection group on the long-term future of the European Union. She is also known for
Vaira_Vīķe-Freiberga
Concept in geometry
Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the order in which they are
Coxeter_element
Topics referred to by the same term
subgroup may refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation
Parabolic_subgroup
2012 single by Marilyn Manson
"No Reflection" is a song by American rock band Marilyn Manson. The track serves as the lead single from the band's eighth studio album, Born Villain.
No_Reflection
under the finite reflection group of a root system. If the reflection group W corresponds to the Weyl group of a compact semisimple group K with maximal
Kostant_polynomial
Rotation composed with a reflection
geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space
Improper_rotation
Real square matrix whose columns and rows are orthogonal unit vectors
bring any orthogonal matrix to the identity; thus an orthogonal group is a reflection group. The last column can be fixed to any unit vector, and each choice
Orthogonal_matrix
Dialogue among traditionalist Catholics in France
The Group for Reflection among Catholics (French: Groupe de réflexion entre catholiques, GREC) is an informal organization for "meetings and discussions
Group for Reflection among Catholics
Group_for_Reflection_among_Catholics
Heisenberg group, discrete Heisenberg group Molecular symmetry Nielsen transformation Reflection group Tarski monster group Thompson groups Tietze transformation
List_of_group_theory_topics
German mathematician
question of whether every finite complex reflection group is a Weyl group of an object analogous to a finite group of Lie type. They baptized the unknown
Gunter_Malle
rotation axis Cn. The C1 group is covered in the nonaxial groups section. The reflection groups are denoted by Cnh. These groups are characterized by i)
List of character tables for chemically important 3D point groups
List_of_character_tables_for_chemically_important_3D_point_groups
Manifold of dimension 3 equipped with a hyperbolic metric
/m,m\in \mathbb {N} } ). Such a polytope gives rise to a Kleinian reflection group, which is a discrete subgroup of isometries of hyperbolic space. Taking
Hyperbolic_3-manifold
Root system associated to a symmetric space
associated with a symmetric space. The associated finite reflection group is called the restricted Weyl group. The restricted root system of a symmetric space
Restricted_root_system
Mathematical function
the ring of invariants of the reflection group. Opdam (1989) gave a uniform proof for all crystallographic reflection groups. Several years later he proved
Selberg_integral
Optical instrument to view patterns due to repeated reflection
displaying short descriptions of redirect targets Reflection group – Discrete group type in group theory Teleidoscope – Optical toy Uniform tilings in
Kaleidoscope
Topics referred to by the same term
Look up reflections or reflexions in Wiktionary, the free dictionary. Reflections may refer to: Reflections; or Sentences and Moral Maxims, a series of
Reflections
group of order 2 is a 3-dimensional complex reflection group of order 2160 generated by 45 complex reflections of order 2. The invariants form a polynomial
Valentiner_group
Initiation room in Freemasonry
Freemasonry, the Chamber of Reflection, often abbreviated as C.O.R., and alternatively known as the Room of Reflection, Reflection Cabinet, or Meditation Cabinet
Chamber_of_Reflection
President of the ICC from 2021 to 2024
2001–2002 he was working as an expert at the Council of Europe in the Reflection Group on developments in international cooperation in criminal matters and
Piotr_Hofmański
Geometric polyhedral group
symmetries double to 24, 48, 120 respectively for the full reflectional groups. The reflection symmetries have 6, 9, and 15 mirrors respectively. The octahedral
Polyhedral_group
24-dimensional repeating pattern of points
two-element reflection group, provides an explicit construction of the Griess algebra that has the monster group as its automorphism group. This monster
Leech_lattice
Classification system for symmetry groups in geometry
is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing
Coxeter_notation
Spanish diplomat and politician (1937–2026)
of the transatlantic agenda. In this last capacity, he chaired the Reflection group set up to prepare the negotiations on treaty change, which led to the
Carlos_Westendorp
2015 studio album by Fifth Harmony
Reflection is the debut studio album by American girl group Fifth Harmony. It was released on January 30, 2015, by Syco Music and Epic Records. Lyrically
Reflection (Fifth Harmony album)
Reflection_(Fifth_Harmony_album)
a complex reflection group". Shephard and Todd derived a full classification of such groups. Let V be one-dimensional. Then any finite group faithfully
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
hyperbolic reflection group), but rather to the ordinary triangle group (the von Dyck group) D(2,3,7) of orientation-preserving maps (the rotation group), which
Hurwitz_surface
construct analogues of Lie groups over finite fields, called Chevalley groups. complex reflection group complex reflection group coroot coroot Coxeter 1
Glossary of Lie groups and Lie algebras
Glossary_of_Lie_groups_and_Lie_algebras
Type of hyperbolic triangle
does not preserve angles. The real ideal triangle group is the reflection group generated by reflections of the hyperbolic plane through the sides of an
Ideal_triangle
American mathematician (born 1949)
Davis–Moussong complex, Davis manifolds, Davis–Januszkiewicz space, and the reflection group trick. Davis attended Princeton University where he earned a bachelor's
Michael_W._Davis
International cooperative community
this occasion, the Ministerial Council also established a High Level Reflection Group, which was mandated to assess the adequacy of the institutional set
Energy_Community
1974 studio album by George Duke
Faces in Reflection is the third studio album by American keyboardist George Duke issued in 1974 on MPS Records. The album reached No. 31 on the Billboard
Faces_in_Reflection
Topics referred to by the same term
function f and a constant a Reflection theorem, one of a collection of theorems about the sizes of class groups Schwarz reflection principle, a way to extend
Reflection principle (disambiguation)
Reflection_principle_(disambiguation)
Polish philosopher (1948–2013)
European Commission on several occasions, most notably as chairman of the Reflection Group The Spiritual and Cultural Dimension of Europe (2002–04). He is chairman
Krzysztof_Michalski
Physical effect used in quantum mechanics
frustrated total internal reflection (FTIR) and is an optical analog of quantum tunneling. Balcou and Dutriaux obtained the group delay from a measurement
Hartman_effect
lines through each point. Its complex reflection group is 3[3]3[3]3 or , order 648, also called a Hessian group. It has 27 copies of , order 24, at each
Hessian_polyhedron
2017 studio album by Silverstein
Dead Reflection is the ninth studio album by the Canadian post-hardcore band Silverstein, released on July 14, 2017 through Rise Records worldwide and
Dead_Reflection
2017 studio album by Brian Eno
Reflection is the twenty-seventh studio album by Brian Eno, released on 1 January 2017 on Warp Records. It is a piece of generative ambient music produced
Reflection_(Brian_Eno_album)
American hip hop duo
Reflection Eternal is an American hip hop duo composed of emcee Talib Kweli and producer Hi-Tek. They released their first album, Train of Thought, in
Reflection_Eternal
2000 American TV series or program
My Reflection, also known as Christina Aguilera: My Reflection or My Reflection: Live, is a television special starring American singer Christina Aguilera
My_Reflection
2013 studio album (Split) by Cough and Windhand
Reflection of the Negative is a split album by American doom metal bands Cough and Windhand. It was released on April 16, 2013 via Relapse Records. "Cough/Windhand
Reflection_of_the_Negative
Unique element of maximal length in a finite Coxeter group
Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections. It
Longest element of a Coxeter group
Longest_element_of_a_Coxeter_group
Evaristo Carvalho. He is a member of the Democratic Convergence Party-Reflection Group (PCD-GR). "DIÁRIO da Assembleia Nacional: Sessão Plenária de 11 de
Francisco da Silva (politician)
Francisco_da_Silva_(politician)
Area of mathematics
Stembridge, John (1989-12-01). "On the eigenvalues of representations of reflection groups and wreath products". Pacific Journal of Mathematics. 140 (2). Mathematical
Representation theory of the symmetric group
Representation_theory_of_the_symmetric_group
Polish academician and diplomat (born 1938)
foreign minister. While in that position, Rotfeld established the Warsaw Reflection Group on UN Reform and the Transformation of the Euro-Atlantic Security Institutions
Adam_Daniel_Rotfeld
One of several theorems linking the sizes of different ideal class groups
In algebraic number theory, a reflection theorem or Spiegelungssatz (German for reflection theorem – see Spiegel and Satz) is one of a collection of theorems
Reflection_theorem
Political party in São Tomé and Príncipe
2002, the party won together with the Democratic Convergence Party-Reflection Group 39.4% of the popular vote and 23 out of 55 seats. The same alliance
Force for Change Democratic Movement – Liberal Party
Force_for_Change_Democratic_Movement_–_Liberal_Party
1960s Detroit blue-eyed soul group
The Reflections are an American blue-eyed soul/doo-wop group from Detroit, Michigan, United States. They had one hit single in 1964 called "(Just Like)
The Reflections (Detroit band)
The_Reflections_(Detroit_band)
Natural number
indexes makes 73 the only Sheldon prime. There are precisely 37 complex reflection groups. In three-dimensional space, the most uniform solids are: the five
37_(number)
Generalization of a polytope in real space
symmetry. For any regular polytope the symmetry group (here a complex reflection group, called a Shephard group) acts transitively on the flags, that is, on
Complex_polytope
REFLECTION GROUP
REFLECTION GROUP
Girl/Female
Tamil
Reflection, Image, Radiance
Boy/Male
Hindu
Reflection
Boy/Male
Indian
Reflection; Gnawing Reflection
Boy/Male
Hindu, Indian
Our Reflection
Boy/Male
Hindu, Indian, Punjabi, Sanskrit, Sikh
Thought; Reflection
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Reflection; Outlook; Reflection Reflection
Boy/Male
Bengali, Hindu, Indian
Image; Reflection
Girl/Female
Indian
Reflection, Image, Radiance
Girl/Female
Tamil
Reflection, Image, Radiance
Boy/Male
Buddhist, Indian, Japanese
Ancient Reflection
Girl/Female
Hindu, Indian
Reflection
Boy/Male
Hindu
Reflection
Boy/Male
Tamil
Reflection
Boy/Male
Hindu, Indian
Perception; Reflection
Girl/Female
Japanese
Mirror reflection.
Girl/Female
Arabic, Assamese, Australian, Hindu, Indian, Marathi, Muslim, Sindhi
Mirror; Reflection
Girl/Female
Indian, Malayalam
Reflection
Girl/Female
Bengali, Hindu, Indian
Reflection; Mirror
Boy/Male
Tamil
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Reflection
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Boy/Male
Tamil
Reflection through study
REFLECTION GROUP
REFLECTION GROUP
Boy/Male
Indian, Sanskrit
Born of Intellect; Another Name for Pururavas
Boy/Male
Tamil
Good boy
Male
English
Short form of English names beginning with Brad-, from Old English brád, BRAD means "broad."
Girl/Female
Indian
Excelling
Boy/Male
Arabic, Muslim
He who is Rewarded
Boy/Male
Hindu
Thunder
Girl/Female
Australian, German, Hebrew, Polish
The Lord is Gracious; Female Version of John
Boy/Male
Hindu, Indian
Conquest
Boy/Male
Hindu, Indian
God Man
Boy/Male
Indian, Sanskrit
Born Twice; Bird
REFLECTION GROUP
REFLECTION GROUP
REFLECTION GROUP
REFLECTION GROUP
REFLECTION GROUP
n.
See Reflection.
n.
A slide, modulation, or accent of the voice; as, the rising and the falling inflection.
a.
Addicted to introspective or meditative habits; as, a reflective person.
a.
Capable of, or pertaining to, flection or inflection.
n.
Want of reflection.
n.
The act of reflecting, or turning or sending back, or the state of being reflected.
a.
Throwing back images; as, a reflective mirror.
n.
That which is produced by reflection.
n.
A device for reflecting sound.
n.
Election beforehand.
n.
A reflecting telescope.
n.
A part reflected, or turned back, at an angle; as, the reflection of a membrane.
a.
Capable of exercising thought or judgment; as, reflective reason.
n.
The return of rays, beams, sound, or the like, from a surface. See Angle of reflection, below.
n.
The variation of words by declension, comparison, or conjugation; inflection.
a.
Given to reflection or serious consideration; reflective; contemplative; as, a reflecting mind.
n.
A deviation of the rays of light toward the surface of an opaque body; inflection; diffraction.
n.
Election a second time, or anew; as, the reelection of a former chief.
n.
An image given back from a reflecting surface; a reflected counterpart.
a.
The act of choosing; choice; selection.