For general access to the Wolfram Knowledgebase, use entities of type Surface instead of SurfaceData.


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


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

SurfaceData[entity, property, annotation]

gives the specified annotation associated with the given property.


  • SurfaceData[] gives a list of all surface entities.
  • SurfaceData["Properties"] gives a list of available properties.
  • SurfaceData["SampleEntities"] gives a list of sample entities.
  • The specified entity in SurfaceData 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:
  • "AlgebraicDegree"algebraic degree
    "AlgebraicEquation"algebraic equation
    "AlternateNames"alternate names
    "AssociatedPeople"associated people
    "CartesianEquation"Cartesian equation
    "Centroid"centroid of solid
    "ChristoffelSymbolOfTheSecondKind"Christoffel symbol of the second kind
    "ChromaticNumber"chromatic number
    "EulerCharacteristic"Euler characteristic
    "FilledRegion"filled region
    "FirstFundamentalForm"coefficients of the first fundamental form
    "GaussianCurvature"Gaussian curvature
    "GeneralizedDiameter"generalized diameter
    "Graphics3D"3D graphics expression
    "ImplicitGaussianCurvature"implicit Gaussian curvature
    "ImplicitMeanCurvature"implicit mean curvature
    "ImplicitNormalVector"implicit normal vector
    "InertiaTensor"moment of inertia tensor of solid
    "LineSegmentLengthCDF"CDF of lengths
    "LineSegmentLengthMean"mean line segment length
    "LineSegmentLengthPDF"PDF of lengths
    "MeanCurvature"mean curvature
    "MetricTensor"metric tensor
    "NodeCount"number of nodes
    "NormalVector"normal vector
    "ParametricEquations"parametric equations
    "PrincipalCurvatures"principal curvatures
    "PunctureCount"number of punctures
    "RelatedWolframLanguageSymbols"related symbols in the Wolfram Language
    "RicciTensor"Ricci tensor
    "RiemannTensor"Riemann tensor
    "SecondFundamentalForm"coefficients of the second fundamental form
    "SemialgebraicDescription"semialgebraic description
    "SingularPoints"singular points
    "SportObjects"sport objects
    "SurfaceArea"surface area
    "VariableConstraints"variable constraints
    "VariableDescriptions"description of variables
    "VectorLength"vector length
    "Volume"volume of solid


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Basic Examples  (8)

Use for entity discovery:

Return a list of sample surface entities:

Use to discover properties of a surface:

Display an image of a surface:

Find properties of a surface:

Return people associated with a surface:

Find a list of sample entity classes of surfaces:

Find surfaces in a given class:

Properties & Relations  (2)

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

Evaluate SurfaceData with "Classes" argument:

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

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  (2)

Color a surface according to its Gaussian curvature:

Display Peano's image on Peano's surface:

Wolfram Research (2014), SurfaceData, Wolfram Language function, (updated 2016).


Wolfram Research (2014), SurfaceData, Wolfram Language function, (updated 2016).


Wolfram Language. 2014. "SurfaceData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016.


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


@misc{reference.wolfram_2024_surfacedata, author="Wolfram Research", title="{SurfaceData}", year="2016", howpublished="\url{}", note=[Accessed: 19-June-2024 ]}


@online{reference.wolfram_2024_surfacedata, organization={Wolfram Research}, title={SurfaceData}, year={2016}, url={}, note=[Accessed: 19-June-2024 ]}