Symmetry Groups

Some articles on groups, group, symmetry groups:

Point Groups In Two Dimensions - More General Groups
... 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 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 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 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 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 ...

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