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...

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

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

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...

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

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...

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

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

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

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

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...

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...

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

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

formed in 2010 The Reflections (Detroit band), a doo-wop group formed in the early 1960s The Reflections (Indianapolis band), a vocal group formed in the early...

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

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

Self-reflection is the ability to witness and evaluate one's own cognitive, emotional, and behavioural processes. In psychology, other terms used for this...

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

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

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

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...

to the line of reflection. Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of...

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...

geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space...

Celebrity Reflection is the fifth, final, and largest Solstice-class cruise ship, her sister ships being Celebrity Equinox, Celebrity Eclipse, Celebrity...

subgroup may refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation...

Reflection of Something is the second label-released album by contemporary Christian songwriter Todd Agnew. The album was released by Ardent Records on...

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...

foreign minister. While in that position, Rotfeld established the Warsaw Reflection Group on the UN Reform and the Transformation of the Euro-Atlantic Security...