### Some articles on *groups, group, symmetry groups*:

Point Groups In Two Dimensions - More General Groups

... These

... These

**groups**are readily constructed with two-dimensional orthogonal matrices ... The continuous cyclic**group**SO(2) or C∞ and its subgroups have elements that are rotation matrices where SO(2) has any possible θ ... For discrete cyclic**groups**Cn, elements Cnk = R(2πk/n) The continuous dihedral**group**O(2) or D∞ and its subgroups with reflections have elements that include not only rotation matrices, but also reflection matrices ...Frieze Group - General

... Formally, a frieze

... Formally, a frieze

**group**is a class of infinite discrete**symmetry groups**for patterns on a strip (infinitely wide rectangle), hence a class of**groups**of isometries of the plane ... There are seven different frieze**groups**... The actual**symmetry groups**within a frieze**group**are characterized by the smallest translation distance, and, for the frieze**groups**4-7, by a shifting parameter ...Orthogonal Group - Related Groups - Discrete Subgroups

... As the orthogonal

... As the orthogonal

**group**is compact, discrete subgroups are equivalent to finite subgroups ... These subgroups are known as point**group**and can be realized as the**symmetry groups**of polytopes ... A very important class of examples are the finite Coxeter**groups**, which include the**symmetry groups**of regular polytopes ...One-dimensional Symmetry Group - Translational Symmetry - Discrete

... We first consider patterns for which the

**Symmetry Groups**... We first consider patterns for which the

**group**is discrete, i.e ... for which the positive values in the**group**have a minimum ... Such patterns fall in two categories, the two 1D space**groups**or line**groups**...List Of Planar

... This article summarizes the classes of discrete planar

**Symmetry Groups**... This article summarizes the classes of discrete planar

**symmetry groups**... The**symmetry groups**are named here by three naming schemes International notation, orbifold notation, and Coxeter notation ... There are three kinds of**symmetry groups**of the plane 2 rosette**groups**– 2D point**groups**7 frieze**groups**– 2D line**groups**17 wallpaper**groups**– 2D ...### Famous quotes containing the words groups and/or symmetry:

“As in political revolutions, so in paradigm choice—there is no standard higher than the assent of the relevant community. To discover how scientific revolutions are effected, we shall therefore have to examine not only the impact of nature and of logic, but also the techniques of persuasive argumentation effective within the quite special *groups* that constitute the community of scientists.”

—Thomas S. Kuhn (b. 1922)

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)

Main Site Subjects

Related Subjects

Related Phrases

Related Words