About: Point groups in two dimensions

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In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group.

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rdfs:label	Rozet (patroon) (nl) Point groups in two dimensions (en)
rdfs:comment	In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group. (en) Een rozet is een tweedimensionaal patroon met alleen rotatiesymmetrie en eventueel spiegelsymmetrie, maar geen translatiesymmetrie. De rozet is een veelgebruikt patroon in de architectuur en de beeldende kunst. Bekend zijn de roosvensters met rozetvormig maaswerk in gotische kathedralen. Zie hieronder diverse voorbeelden van o.a. verkeersborden en vlaggen met een rozetpatroon. Cyclische groepen bevatten alleen rotatiesymmetrie. De groep wordt onderverdeeld door het aantal sectoren waaruit het patroon is opgebouwd. De naamgeving is Cn waarin n = 2, 3, 4, 5... (nl)
foaf:depiction
dcterms:subject	Euclidean symmetries Group theory
Wikipage page ID	3037988 (xsd:integer)
Wikipage revision ID	980334532 (xsd:integer)
Link from a Wikipage to another Wikipage	One-dimensional symmetry group Euclidean symmetries Vector field Point group Transversality (mathematics) Group theory Countable set Coxeter notation Quotient group Geometry Crystallographic point group Crystallographic restriction theorem Crystallography Starfish Frieze group Kernel (algebra) Subgroup Symmetry Symmetry group Topological group Wallpaper group Lattice (group) Line group Cyclic group Flower Glide reflection Reflection (mathematics) Group (mathematics) Group homomorphism Rigid transformation Medusozoa Surjective Hermann–Mauguin notation Homogeneity (physics) DIH Square (geometry) Circle group Circular symmetry Orbifold Orthogonal group Orthogonal matrix Semidirect product Rotation Unitary group Point groups in four dimensions Point groups in three dimensions Finitely generated abelian group dbr:Hermann–Mauguin_symbol
Link from a Wikipage to an external page	http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node9.html http://www.math.ttu.edu/~drager/Classes/10MathCamp/handouts04.pdf https://web.archive.org/web/20121024123235/http:/www.stanford.edu/~yishuwei/crystal.pdf
sameAs	Point groups in two dimensions Point groups in two dimensions Point groups in two dimensions Point groups in two dimensions Point groups in two dimensions
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has abstract	In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group. The two-dimensional point groups are important as a basis for the axial three-dimensional point groups, with the addition of reflections in the axial coordinate. They are also important in symmetries of organisms, like starfish and jellyfish, and organism parts, like flowers. (en) Een rozet is een tweedimensionaal patroon met alleen rotatiesymmetrie en eventueel spiegelsymmetrie, maar geen translatiesymmetrie. De rozet is een veelgebruikt patroon in de architectuur en de beeldende kunst. Bekend zijn de roosvensters met rozetvormig maaswerk in gotische kathedralen. Zie hieronder diverse voorbeelden van o.a. verkeersborden en vlaggen met een rozetpatroon. Cyclische groepen bevatten alleen rotatiesymmetrie. De groep wordt onderverdeeld door het aantal sectoren waaruit het patroon is opgebouwd. De naamgeving is Cn waarin n = 2, 3, 4, 5... Dihedrale groepen bevatten naast rotatiesymmetrie ook spiegelsymmetrie. De naamgeving is Dn waarin n = 2, 3, 4, 5... Het is mogelijk de rozetsymmetrie uit te breiden naar drie dimensies. De groepen die dit beschrijven worden puntgroepen genoemd en spelen een belangrijke rol in de beschrijving van chemische moleculen, al of niet als onderdeel van de beschrijving van kristalstructuren en hun ruimtegroepen. (nl)
gold:hypernym	Group
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foaf:isPrimaryTopicOf	wikipedia-en:Point_groups_in_two_dimensions
is Link from a Wikipage to another Wikipage of	List of finite spherical symmetry groups One-dimensional symmetry group List of geometry topics Point group Line group Isometry group Reflection group DIH Space group

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