# Lattice

Related Interpreter »
Notable mathematical lattices.

Entity["Lattice",name] or

represents an entity of type "Lattice".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["Lattice",{propispeci,}]

represents a class of entities with values of propi defined by speci.

# Properties

•  AlternateNames alternate names AutomorphismGroupOrder number of symmetries Basis basis CenterDensity center density Classes classes CoveringRadius covering radius CoxeterNumber Coxeter number CrystalFamily crystal family CrystalSystems crystal system Density density Determinant determinant Dimension dimension Dual dual EntityClasses entity classes Even even Extremal extremal GeneratorMatrix generator matrix GramMatrix Gram matrix Graphics3D 3D graphic HermiteInvariant Hermite invariant Image image Integral integral KissingNumber kissing number LatticeSystem lattice system MinimalNorm minimal squared norm MinimalVectors smallest vectors ModularNumber modular number Name name Nonextremal nonextremal Nonintegral nonintegral Nonunimodular nonunimodular Notation notation Odd odd PackingRadius packing radius QuadraticForm quadratic form RadialFunction radial function ThetaSeriesFunction theta series Thickness thickness Unimodular unimodular Volume volume

# Details

• "Lattice" entities include particular named mathematical lattices as well as members of parametrized families.
• "Lattice" entity classes include classifications based on various mathematical properties.
• Some properties are available for the "Lattice" entity type as a whole and can be given using the form EntityValue["Lattice",property]. Such properties include:
•  "Properties" the list of available properties "PropertyCanonicalNames" the standard names of available properties "SampleEntities" a sample list of available entities (typically of length 10) "SampleEntityClasses" a sample list of available entity classes (typically of length 10) "EntityCount" number of entities available "Entities" the list of available entities "EntityCanonicalNames" the standard names of available entities "EntityClasses" the list of available entity classes "EntityClassCanonicalNames" the standard names of available entity classes "PropertyClasses" the list of available property classes "PropertyClassCanonicalNames" the standard names of available property classes "PropertyCount" number of properties available
• The following annotations can be used in the third argument of EntityValue["Lattice",property,annotation]:
•  "EntityAssociation" an association of entities and entity-property values "PropertyAssociation" an association of properties and entity-property values "EntityPropertyAssociation" an association in which the specified entities are keys, and values are a nested association of properties and entity-property values "PropertyEntityAssociation" an association in which the specified properties are keys, and values are a nested association of entities and entity-property values "Dataset" a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
• The following annotations can be used in the second argument of EntityValue[property,annotation]:
•  "Description" a brief textual description of the property

# Examples

## Basic Examples(4)

Use for entity discovery:

Find a property value for an entity:

Retrieve a dataset of all available properties for an entity:

Return lattices in three dimensions: