About: Periodic graph (geometry)

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A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas.

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rdf:type	yago:Abstraction100002137 yago:Communication100033020 yago:Graph107000195 yago:WikicatGeometricGraphs yago:VisualCommunication106873252
rdfs:label	Periodic graph (geometry) (en)
rdfs:comment	A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas. (en)
dct:subject	Geometric graphs
Wikipage page ID	29008597 (xsd:integer)
Wikipage revision ID	1076596015 (xsd:integer)
Link from a Wikipage to another Wikipage	Schläfli symbol Basis (linear algebra) Boris Delaunay Geometric graphs Cycle (graph theory) Degree (graph theory) Line segment Prototile Geometric graph theory Geometric group theory Net (polyhedron) Quasicrystal N-skeleton Coordination sequence Crystal engineering Crystal structure prediction Homotopic Ludwig Bieberbach Fundamental domain Triply periodic minimal surface Three-dimensional Glass Polynomial-time reduction Minimal surface Euclidean space Evgraf Fedorov Discrete geometry Hilbert's eighteenth problem Isomorphism (crystallography) Hyperbolic geometry Symmetry groups Translation (geometry) Discrete space CW complex Space group Polynomial time Tessellation of space Set (mathematics) Gyroid Zeolite Schwarz minimal surface Polytope Schoenflies Periodic Graphs (Crystallography) Vlsi Crystal net
sameAs	Periodic graph (geometry) Periodic graph (geometry) Periodic graph (geometry) Periodic graph (geometry)
dbp:wikiPageUsesTemplate	dbt:! dbt:Citation dbt:Other_uses dbt:Reflist
has abstract	A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas. Much of the effort in periodic graphs is motivated by applications to natural science and engineering, particularly of three-dimensional crystal nets to crystal engineering, crystal prediction (design), and modeling crystal behavior. Periodic graphs have also been studied in modeling very-large-scale integration (VLSI) circuits. (en)
prov:wasDerivedFrom	wikipedia-en:Periodic_graph_(geometry)?oldid=1076596015&ns=0
page length (characters) of wiki page	18151 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Periodic_graph_(geometry)
is Link from a Wikipage to another Wikipage of	Periodic graph (crystallography) Periodic Graph (Geometry) Ludwig Bieberbach Periodic graph Discrete geometry List of Russian mathematicians List of Russian scientists List of Tokyo Institute of Technology people Laves graph List of Russian people Periodic Graphs (Geometry)
is Wikipage redirect of	Periodic Graph (Geometry) Periodic Graphs (Geometry)
is Wikipage disambiguates of	Periodic graph
is foaf:primaryTopic of	wikipedia-en:Periodic_graph_(geometry)

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