For general access to the Wolfram Knowledgebase, use entities of type Lamina instead of LaminaData.


gives the value of the specified property for the lamina entity.


gives a list of property values for the specified lamina entities.


gives the specified annotation associated with the given property.


  • LaminaData[] gives a list of all lamina entities.
  • LaminaData["Properties"] gives a list of available properties.
  • LaminaData["SampleEntities"] gives a list of sample entities.
  • The specified entity in LaminaData can be an Entity, EntityClass, entity canonical name, or list thereof.
  • The specified property can be an EntityProperty, EntityPropertyClass, property canonical name, or list of properties.
  • Properties that do not apply or are not known in a particular case are indicated by Missing[].
  • Properties include:
  • "AlternateNames"alternate names
    "AngleCount"number of angles
    "AreaMomentOfInertiaTensor"area moment of inertia tensor
    "AreaMomentOfInertiaXX"area moment of inertia about the axis
    "AreaMomentOfInertiaXY"product moment of inertia
    "AreaMomentOfInertiaYY"area moment of inertia about the axis
    "AreaMomentOfInertiaZZ"polar moment of inertia
    "AssociatedEntities"associated entities
    "AssociatedPeople"associated people
    "BoundaryCurve"boundary curve
    "BoundaryDiagram"boundary diagram
    "BoundaryMeshRegion"boundary mesh representation
    "BoundingBox"corners of bounding box
    "CircumcenterOfMass"circumcenter of mass
    "ConvexityCoefficient"convexity coefficient
    "DiagonalCount"number of diagonals
    "DiagonalizedAreaMomentOfInertiaTensor"diagonalized area moment of inertia tensor
    "DiagonalLengths"diagonal lengths
    "EdgeCount"number of edges
    "EdgeLengths"side lengths
    "GeneralizedDiameter"generalized diameter
    "Graphics"graphics expression
    "HoleCount"number of holes
    "ImplicitRegion"implicit region
    "Inequalities"defining inequalities
    "InteriorAngles"interior angles
    "InteriorAngleSum"interior angle sum
    "LineOfSymmetryCount"number of lines of symmetry
    "LineSegmentLengthCDF"CDF of lengths
    "LineSegmentLengthMean"mean line segment length
    "LineSegmentLengthPDF"PDF of lengths
    "MajorAxis"major axis length (major diameter)
    "MinorAxis"minor axis length (minor diameter)
    "MeshRegion"mesh representation
    "RadiiOfGyration"radii of gyration about coordinate axes
    "RadiusOfGyrationX"radius of gyration about the axis
    "RadiusOfGyrationY"radius of gyration about the axis
    "RealWorldExamples"real-world examples
    "RelatedWolframLanguageSymbols"related symbols in the Wolfram Language
    "RightAngleCount"number of internal right angles
    "SectionModuli"section moduli
    "SectionModulusX"section modulus about the axis
    "SectionModulusY"section modulus about the axis
    "SemimajorAxis"semimajor axis length (major radius)
    "SemiminorAxis"semiminor axis length (minor radius)
    "SportObjects"sport objects of given shape
    "TorsionalRigidityMultiplier"torsional rigidity multiplier for solid bar
    "TriangleAreaCDF"CDF of triangle areas
    "TriangleAreaMean"mean triangle area
    "TriangleAreaPDF"PDF of triangle areas
    "TriangulationCount"number of triangulations
    "VariableConstraints"variable constraints
    "VariableDescriptions"variable descriptions
    "VertexCount"number of vertices


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Basic Examples  (11)

Use for entity discovery:

Return a list of sample lamina entities:

Use to discover properties of a lamina:

Display a diagram of a lamina:

Find the properties of a lamina:

Return people associated with a lamina:

Create a table of variables determining the shape of a lamina, together with their descriptions:

Find classes of lamina:

Find lamina in a given class:

Diagrams and equations of area for a class of lamina:

Give a geometric region corresponding to an annulus:

Discretize and visualize the region:

Give an implicit geometric region corresponding to a square I-beam:

Discretize and visualize the implicit region:

Properties & Relations  (2)

Using LaminaData is equivalent to calling EntityValue on the corresponding entity and property:

Evaluate LaminaData with "Classes" argument:

The above is equivalent to evaluating EntityClassList of the entity type "Lamina":

Possible Issues  (1)

Entity classes cannot be given as bare strings:

Specifying an explicit EntityClass works as intended:

This is equivalent to calling EntityList on the EntityClass:

Neat Examples  (1)

Draw a lamina together with its incircle and circumcircle:

Wolfram Research (2014), LaminaData, Wolfram Language function, (updated 2019).


Wolfram Research (2014), LaminaData, Wolfram Language function, (updated 2019).


Wolfram Language. 2014. "LaminaData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019.


Wolfram Language. (2014). LaminaData. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_laminadata, author="Wolfram Research", title="{LaminaData}", year="2019", howpublished="\url{}", note=[Accessed: 24-July-2024 ]}


@online{reference.wolfram_2024_laminadata, organization={Wolfram Research}, title={LaminaData}, year={2019}, url={}, note=[Accessed: 24-July-2024 ]}