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...

In the mathematical theory of reflection groups, the parabolic subgroups are a special kind of subgroup. The precise definition of which subgroups are...

a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial...

point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among...

Coxeter groups are precisely the finite Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter group. However...

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest...

translations, rotations, reflections, and glide reflections (see below § Classification). The set of Euclidean plane isometries forms a group under composition:...

or it is a reflection or improper rotation (determinant of M = −1). The geometric symmetries of crystals are described by space groups, which allow...

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...

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...

The Democratic Convergence Party-Reflection Group (Portuguese: Partido de Convergência Democrática-Grupo de Reflexão), or PCD-GR, is a political party...

space groups (which describe e.g. crystal symmetries). Objects with glide-reflection symmetry are in general not symmetrical under reflection alone,...

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...

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...

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...

Mirrors and Reflections: The Geometry of Finite Reflection Groups is an undergraduate-level textbook on the geometry of reflection groups. It was written...

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 groups have close relationships with other mathematical objects, including juggling patterns and certain complex reflection groups. Many of their...

plane symmetry groups: Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through...

Reflection map may refer to: Reflection mapping in computer graphics A reflection (mathematics), specifically an element of a reflection group an element...

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...

Jens Stoltenberg appointed Mitchell co-chair of NATO's high-level Reflection Group, a commission of senior experts tasked with providing recommendations...

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...

as the symmetry group of a non-square rectangle (with the three non-identity elements being horizontal reflection, vertical reflection and 180-degree rotation)...

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...

algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. Various properties of the Dynkin...

(e-IRGSP5), Leibniz Universität Hannover, Germany e-Infrastructure Reflection Group home page e-Infrastructure EU Competitiveness Council Conclusions,...

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...

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...

fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular...