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- Point_group abstract "In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y: y = Mxwhere the origin is the fixed point. Point-group elements can either be rotations (determinant of M = 1) or else reflections, or improper rotations (determinant of M = −1).Discrete point groups in more than one dimension come in infinite families, but from the crystallographic restriction theorem and one of Bieberbach's theorems, each number of dimensions has only a finite number of point groups that are symmetric over some lattice or grid with that number. These are the crystallographic point groups.".
- Point_group thumbnail Flag_of_Hong_Kong.svg?width=300.
- Point_group wikiPageExternalLink sieve.
- Point_group wikiPageExternalLink node45.html.
- Point_group wikiPageExternalLink node9.html.
- Point_group wikiPageExternalLink index.html.
- Point_group wikiPageExternalLink productCd-0471010030.html.
- Point_group wikiPageID "1138942".
- Point_group wikiPageRevisionID "564607179".
- Point_group hasPhotoCollection Point_group.
- Point_group subject Category:Crystallography.
- Point_group subject Category:Euclidean_symmetries.
- Point_group subject Category:Group_theory.
- Point_group type Abstraction100002137.
- Point_group type Attribute100024264.
- Point_group type EuclideanSymmetries.
- Point_group type Property104916342.
- Point_group type SpatialProperty105062748.
- Point_group type Symmetry105064827.
- Point_group comment "In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y: y = Mxwhere the origin is the fixed point.".
- Point_group label "Groupe ponctuel de symétrie".
- Point_group label "Grupo puntual".
- Point_group label "Point group".
- Point_group label "Punktgruppe".
- Point_group label "Puntgroep".
- Point_group label "Точечная группа симметрии".
- Point_group label "点群".
- Point_group label "點群".
- Point_group sameAs Punktgruppe.
- Point_group sameAs Grupo_puntual.
- Point_group sameAs Groupe_ponctuel_de_symétrie.
- Point_group sameAs 点群.
- Point_group sameAs 점군.
- Point_group sameAs Puntgroep.
- Point_group sameAs m.049nm2.
- Point_group sameAs Q899720.
- Point_group sameAs Q899720.
- Point_group sameAs Point_group.
- Point_group wasDerivedFrom Point_group?oldid=564607179.
- Point_group depiction Flag_of_Hong_Kong.svg.
- Point_group isPrimaryTopicOf Point_group.
