Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Point_groups_in_three_dimensions> ?p ?o }
- Point_groups_in_three_dimensions abstract "In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries.Symmetry groups of objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetries. All isometries of a bounded 3D object have one or more common fixed points. We choose the origin as one of them.The symmetry group of an object is sometimes also called full symmetry group, as opposed to its rotation group or proper symmetry group, the intersection of its full symmetry group and the rotation group SO(3) of the 3D space itself. The rotation group of an object is equal to its full symmetry group if and only if the object is chiral.The point groups in three dimensions are heavily used in chemistry, especially to describe the symmetries of a molecule and of molecular orbitals forming covalent bonds, and in this context they are also called molecular point groups.Finite Coxeter groups are a special set of point groups generated purely by a set of reflectional mirrors passing through the same point. A rank n Coxeter group has n mirrors and is represented by a Coxeter-Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram, with markup symbols for rotational and other subsymmetry point groups.".
- Point_groups_in_three_dimensions wikiPageExternalLink books?id=9BY9AAAAIAAJ&pg=PA73.
- Point_groups_in_three_dimensions wikiPageExternalLink Simplest.html.
- Point_groups_in_three_dimensions wikiPageExternalLink CC_All.html.
- Point_groups_in_three_dimensions wikiPageExternalLink Solids.html.
- Point_groups_in_three_dimensions wikiPageExternalLink node45.html.
- Point_groups_in_three_dimensions wikiPageExternalLink crystal.pdf.
- Point_groups_in_three_dimensions wikiPageID "2694525".
- Point_groups_in_three_dimensions wikiPageLength "54097".
- Point_groups_in_three_dimensions wikiPageOutDegree "279".
- Point_groups_in_three_dimensions wikiPageRevisionID "677796552".
- Point_groups_in_three_dimensions wikiPageWikiLink 2D_crystallographic_group.
- Point_groups_in_three_dimensions wikiPageWikiLink ADE_classification.
- Point_groups_in_three_dimensions wikiPageWikiLink Abelian_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Alternating_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Antiprism.
- Point_groups_in_three_dimensions wikiPageWikiLink Arthur_Moritz_Schoenflies.
- Point_groups_in_three_dimensions wikiPageWikiLink Arthur_Moritz_Schönflies.
- Point_groups_in_three_dimensions wikiPageWikiLink Binary_cyclic_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Binary_dihedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Binary_icosahedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Binary_octahedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Binary_tetrahedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Bipyramid.
- Point_groups_in_three_dimensions wikiPageWikiLink Category:Euclidean_symmetries.
- Point_groups_in_three_dimensions wikiPageWikiLink Category:Group_theory.
- Point_groups_in_three_dimensions wikiPageWikiLink Chiral_ligand.
- Point_groups_in_three_dimensions wikiPageWikiLink Chirality_(mathematics).
- Point_groups_in_three_dimensions wikiPageWikiLink Closed_(topology).
- Point_groups_in_three_dimensions wikiPageWikiLink Closed_set.
- Point_groups_in_three_dimensions wikiPageWikiLink Compound_of_five_tetrahedra.
- Point_groups_in_three_dimensions wikiPageWikiLink Concanavalin_A.
- Point_groups_in_three_dimensions wikiPageWikiLink Cone.
- Point_groups_in_three_dimensions wikiPageWikiLink Conic_solid.
- Point_groups_in_three_dimensions wikiPageWikiLink Conjugacy_class.
- Point_groups_in_three_dimensions wikiPageWikiLink Coordination_complex.
- Point_groups_in_three_dimensions wikiPageWikiLink Coordination_compound.
- Point_groups_in_three_dimensions wikiPageWikiLink Correspondence_theorem_(group_theory).
- Point_groups_in_three_dimensions wikiPageWikiLink Covalent_bond.
- Point_groups_in_three_dimensions wikiPageWikiLink Covering_space.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter-Dynkin_diagram.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter_diagram.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter_element.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter_notation.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter_number.
- Point_groups_in_three_dimensions wikiPageWikiLink Coxeter–Dynkin_diagram.
- Point_groups_in_three_dimensions wikiPageWikiLink Crystal_system.
- Point_groups_in_three_dimensions wikiPageWikiLink Crystallographic_restriction_theorem.
- Point_groups_in_three_dimensions wikiPageWikiLink Crystallography.
- Point_groups_in_three_dimensions wikiPageWikiLink Cube.
- Point_groups_in_three_dimensions wikiPageWikiLink Cube_(geometry).
- Point_groups_in_three_dimensions wikiPageWikiLink Cycle_diagram.
- Point_groups_in_three_dimensions wikiPageWikiLink Cycle_graph_(algebra).
- Point_groups_in_three_dimensions wikiPageWikiLink Cyclic_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Cyclic_symmetries.
- Point_groups_in_three_dimensions wikiPageWikiLink Cyclic_symmetry_in_three_dimensions.
- Point_groups_in_three_dimensions wikiPageWikiLink Cylinder_(geometry).
- Point_groups_in_three_dimensions wikiPageWikiLink Dicyclic_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Dihedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Dihedral_symmetry.
- Point_groups_in_three_dimensions wikiPageWikiLink Dihedral_symmetry_in_three_dimensions.
- Point_groups_in_three_dimensions wikiPageWikiLink Dihedron.
- Point_groups_in_three_dimensions wikiPageWikiLink Direct_product_of_groups.
- Point_groups_in_three_dimensions wikiPageWikiLink Disdyakis_triacontahedron.
- Point_groups_in_three_dimensions wikiPageWikiLink Dodecahedron.
- Point_groups_in_three_dimensions wikiPageWikiLink Du_Val_singularity.
- Point_groups_in_three_dimensions wikiPageWikiLink Euclidean_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Euclidean_plane_isometry.
- Point_groups_in_three_dimensions wikiPageWikiLink Euler_characteristic.
- Point_groups_in_three_dimensions wikiPageWikiLink File:Volleyball_seams_diagram.png.
- Point_groups_in_three_dimensions wikiPageWikiLink Finite_Coxeter_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Free_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Frieze_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Fundamental_domain.
- Point_groups_in_three_dimensions wikiPageWikiLink Galois_connection.
- Point_groups_in_three_dimensions wikiPageWikiLink Geometry.
- Point_groups_in_three_dimensions wikiPageWikiLink Group_action.
- Point_groups_in_three_dimensions wikiPageWikiLink Group_order.
- Point_groups_in_three_dimensions wikiPageWikiLink Hermann–Mauguin_notation.
- Point_groups_in_three_dimensions wikiPageWikiLink Homotetramer.
- Point_groups_in_three_dimensions wikiPageWikiLink Hurwitz_quaternion.
- Point_groups_in_three_dimensions wikiPageWikiLink Icosahedral_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Icosahedral_symmetry.
- Point_groups_in_three_dimensions wikiPageWikiLink Icosahedron.
- Point_groups_in_three_dimensions wikiPageWikiLink If_and_only_if.
- Point_groups_in_three_dimensions wikiPageWikiLink Improper_rotation.
- Point_groups_in_three_dimensions wikiPageWikiLink Index_of_a_subgroup.
- Point_groups_in_three_dimensions wikiPageWikiLink Inverse_(mathematics).
- Point_groups_in_three_dimensions wikiPageWikiLink Inversion_in_a_point.
- Point_groups_in_three_dimensions wikiPageWikiLink Involution_(mathematics).
- Point_groups_in_three_dimensions wikiPageWikiLink Isometry.
- Point_groups_in_three_dimensions wikiPageWikiLink Isometry_group.
- Point_groups_in_three_dimensions wikiPageWikiLink Isomorphic.
- Point_groups_in_three_dimensions wikiPageWikiLink Isomorphism.
- Point_groups_in_three_dimensions wikiPageWikiLink Kaleidoscope.
- Point_groups_in_three_dimensions wikiPageWikiLink Lattice_theorem.
- Point_groups_in_three_dimensions wikiPageWikiLink Lens_space.
- Point_groups_in_three_dimensions wikiPageWikiLink Lipschitz_quaternion.
- Point_groups_in_three_dimensions wikiPageWikiLink List_of_character_tables_for_chemically_important_3D_point_groups.