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SolidRegionQ[reg]

gives True if the 3D region reg is a solid region and False otherwise.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Special Regions  
Formula Regions  
Mesh Regions  
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Derived Regions  
Geographic Regions  
CSG Regions  
Subdivision Regions  
Possible Issues  
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SolidRegionQ

SolidRegionQ[reg]

gives True if the 3D region reg is a solid region and False otherwise.

Details

  • A solid region is also known as filled 3D region.
  • A solid region is a region with embedding dimension 3 and geometry dimension 3 and no lower-dimensional component.

Examples

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Basic Examples  (3)

Special regions:

Wolfram Language code: SolidRegionQ[Ball[]]
Wolfram Language code: SolidRegionQ[Ball[{x, y, z}]]

Formula regions:

Wolfram Language code: SolidRegionQ[ImplicitRegion[x ^ 2 + y ^ 2 + z ^ 2 ≤ 1, {x, y, z}]]
Wolfram Language code: SolidRegionQ[ImplicitRegion[x ^ 2 + y ^ 2 + z ^ 2 == 1, {x, y, z}]]

Mesh regions:

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {25, 3}]]
Wolfram Language code: SolidRegionQ[ℛ]
Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {25, 3}]]
Wolfram Language code: SolidRegionQ[ℛ]

Scope  (13)

Special Regions  (1)

Solid regions in including Tetrahedron:

Wolfram Language code: ℛ = Tetrahedron[{{1, 0, 0}, {1, 0, 1}, {1, 1, 1}, {0, 0, 1}}]; Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

Cylinder:

Wolfram Language code: ℛ = Cylinder[{{0, 0, 0}, {1, 1, 1}}, 2]; Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

Cuboid:

Wolfram Language code: ℛ = Cuboid[{0, 0, 0}]; Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

Formula Regions  (2)

A ball represented as an ImplicitRegion:

Wolfram Language code: SolidRegionQ[ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}]]

A cylinder:

Wolfram Language code: SolidRegionQ[ImplicitRegion[x^2 + y^2 ≤ 1, {x, y, {z, 0, 2}}]]

ImplicitRegion can have several components of different dimension:

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1∨x == y == z, {x, y, z}];
Wolfram Language code: Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

Mesh Regions  (2)

MeshRegion in 1D:

Wolfram Language code: DelaunayMesh[RandomReal[1, {10, 1}]]
Wolfram Language code: SolidRegionQ[%]

2D:

Wolfram Language code: DelaunayMesh[RandomReal[1, {50, 2}]]
Wolfram Language code: SolidRegionQ[%]

3D:

Wolfram Language code: DelaunayMesh[RandomReal[1, {100, 3}]]
Wolfram Language code: SolidRegionQ[%]

BoundaryMeshRegion in 1D:

Wolfram Language code: ConvexHullMesh[RandomReal[1, {10, 1}]]
Wolfram Language code: SolidRegionQ[%]

2D:

Wolfram Language code: ConvexHullMesh[RandomReal[1, {50, 2}]]
Wolfram Language code: SolidRegionQ[%]

3D:

Wolfram Language code: ConvexHullMesh[RandomReal[1, {50, 3}]]
Wolfram Language code: SolidRegionQ[%]

Derived Regions  (4)

RegionIntersection of two regions:

Wolfram Language code: ℛ = RegionIntersection[Disk[{0, 0}, 1], Disk[{0, 1}, 1]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

RegionUnion of mixed-dimensional regions:

Wolfram Language code: ℛ1 = ParametricRegion[{u, v, w}, {{u, 0, 2}, {v, 0, 2}, {w, 0, 2}}]; ℛ2 = ParametricRegion[{u + 1, v + 1, w + 1}, {{u, 0, 2}, {v, 0, 2}, {w, 0, 2}}]; ℛ = RegionUnion[ℛ1, ℛ2];
Wolfram Language code: Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

TransformedRegion:

Wolfram Language code: ℛ = TransformedRegion[Cuboid[], ScalingTransform[{3, 2, 1}]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: SolidRegionQ[ℛ]

RegionBoundary:

Wolfram Language code: Subscript[ℛ, 1] = Ball[]; Subscript[ℛ, 2] = RegionBoundary[Subscript[ℛ, 1]]
Wolfram Language code: {SolidRegionQ[Subscript[ℛ, 1]], SolidRegionQ[Subscript[ℛ, 2]]}

Geographic Regions  (2)

Polygon with GeoPosition:

Wolfram Language code: ℛ = Polygon[GeoPosition[{{{40.083441, -88.235716}, {40.083607, -88.257488}, {40.082603, -88.257149}, {40.076136999999996, -88.25740499999999}, {40.076178, -88.270888}, {40.076516, -88.271558}, {40.083686, -88.271512}, {40.083659999999995, -88.267046}, ... 33323}, {40.098112, -88.228687}, {40.095216, -88.228627}, {40.095179, -88.238547}, {40.094480999999995, -88.238546}, {40.094508999999995, -88.23267}, {40.094106, -88.232556}, {40.090666999999996, -88.232477}, {40.090741, -88.235745}}}]];
Wolfram Language code: SolidRegionQ[ℛ]

Polygons with GeoPositionXYZ:

Wolfram Language code: ℛ = Polygon[GeoPositionXYZ[{{{150451.6968462432, -4.884430486484052*^6, 4.085078564164219*^6}, {148595.27532671497, -4.884475441490381*^6, 4.085092666620835*^6}, {148626.35829777512, -4.884546311005128*^6, 4.0850073717259285*^6}, {148618.5908634042 ... 7*^6, 4.0860187668081024*^6}, {150697.56410771207, -4.8836599487428395*^6, 4.085984535480795*^6}, {150711.88303095422, -4.883905546449982*^6, 4.0856924143435075*^6}, {150433.15479548014, -4.883908845676418*^6, 4.0856987003255524*^6}}}]];
Wolfram Language code: SolidRegionQ[ℛ]

Polygons with GeoPositionENU:

Wolfram Language code: ℛ = Polygon[GeoPositionENU[{{{3378.2547059731055, -3369.2234780923936, -0.7440009205072329}, {1521.3211635380246, -3351.391253626573, -0.022340134218666208}, {1550.2571145363192, -3462.8657556618973, -0.08899812728964207}, {1528.5672303494055, -418 ... 63383291193, -0.37494203351275246}, {3654.121991908476, -2566.7472331234085, -0.5214977847472255}, {3375.420726854886, -2558.6597093173914, -0.3648706331350695}}}, GeoPosition[{40.11379115639895, -88.2753251202516, -1.0415787873318691}]]];
Wolfram Language code: SolidRegionQ[ℛ]

Polygons with GeoGridPosition:

Wolfram Language code: ℛ = Polygon[GeoGridPosition[{{{-0.9950503945490105, 1.2366760550756015}, {-0.9952074890903578, 1.2369207053693891}, {-0.9952196732768064, 1.2369073327446167}, {-0.9953160063787643, 1.236848436956935}, {-0.9954141759436825, 1.2369993898475449}, {-0. ... 197645333103}, {-0.9949098578570917, 1.2368130881428654}, {-0.9948663952535768, 1.2367477711687371}, {-0.9948714472169538, 1.2367426500757825}, {-0.9949211061652593, 1.2367089232486177}, {-0.9949439717990124, 1.236746107097628}}}, "Bonne"]];
Wolfram Language code: SolidRegionQ[ℛ]

CSG Regions  (1)

CSGRegion in 2D:

Wolfram Language code: CSGRegion["Difference", {Disk[], Disk[{1 / 2, 1 / 2}]}]
Wolfram Language code: SolidRegionQ[%]

3D:

Wolfram Language code: CSGRegion["Difference", {Cube[2], Cylinder[{{1, 1, 1}, {1, -1, 1}}]}]
Wolfram Language code: SolidRegionQ[%]

Subdivision Regions  (1)

SubdivisionRegion in 2D:

Wolfram Language code: SubdivisionRegion[RegionBoundary[Rectangle[]]]
Wolfram Language code: SolidRegionQ[%]

3D:

Wolfram Language code: SubdivisionRegion[Tetrahedron[]]
Wolfram Language code: SolidRegionQ[%]

Possible Issues  (1)

Nonconstant regions are not SolidRegionQ:

Wolfram Language code: SolidRegionQ[Ball[{x, y, z}]]
Wolfram Research (2016), SolidRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidRegionQ.html.

Text

Wolfram Research (2016), SolidRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidRegionQ.html.

CMS

Wolfram Language. 2016. "SolidRegionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SolidRegionQ.html.

APA

Wolfram Language. (2016). SolidRegionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SolidRegionQ.html

BibTeX

@misc{reference.wolfram_2026_solidregionq, author="Wolfram Research", title="{SolidRegionQ}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/SolidRegionQ.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_solidregionq, organization={Wolfram Research}, title={SolidRegionQ}, year={2016}, url={https://reference.wolfram.com/language/ref/SolidRegionQ.html}, note=[Accessed: 12-June-2026]}