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ShellRegion[reg]

gives a solid shell of a 3D region reg.

ShellRegion[reg,t]

gives a solid shell of reg with minimal thickness t.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Special Regions  
Formula Regions  
Mesh Regions  
Applications  
Properties & Relations  
Possible Issues  
See Also
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ShellRegion

ShellRegion[reg]

gives a solid shell of a 3D region reg.

ShellRegion[reg,t]

gives a solid shell of reg with minimal thickness t.

Details

  • ShellRegion is typically used to hollow out a solid to save material when printing a 3D object.
  • ShellRegion preserves the outer surface of an object.

Examples

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Basic Examples  (2)

Find the shell of a ball:

Wolfram Language code: 𝒮 = ShellRegion[Ball[]]
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Find the shell of a mesh region:

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {100, 3}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

Specify a thickness:

Wolfram Language code: 𝒮 = ShellRegion[ℛ, 0.25];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

Scope  (16)

Basic Uses  (3)

ShellRegion works on solid regions:

Wolfram Language code: ShellRegion[Ball[]]

Closed surfaces:

Wolfram Language code: ShellRegion[Sphere[]]

Specify a thickness for a shell:

Wolfram Language code: ShellRegion[Ball[], 3 / 4]

Special Regions  (8)

Find the shell of a Ball:

Wolfram Language code: 𝒮 = ShellRegion[Ball[]]
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Cuboid:

Wolfram Language code: 𝒮 = ShellRegion[Cuboid[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Hexahedron:

Wolfram Language code: 𝒮 = ShellRegion[Hexahedron[{{0, 0, 0}, {1, 0, 0}, {2, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}, {2, 1, 1}, {1, 1, 1}}]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Parallelepiped:

Wolfram Language code: 𝒮 = ShellRegion[Parallelepiped[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Prism:

Wolfram Language code: 𝒮 = ShellRegion[Prism[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Pyramid:

Wolfram Language code: 𝒮 = ShellRegion[Pyramid[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Simplex:

Wolfram Language code: 𝒮 = ShellRegion[Simplex[{{0, 0, 0}, {1, 1, 1}, {2, 1, 0}, {1, 0, 0}}]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Tetrahedron:

Wolfram Language code: 𝒮 = ShellRegion[Tetrahedron[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Formula Regions  (2)

Find the shell of an ImplicitRegion:

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}];
Wolfram Language code: 𝒮 = ShellRegion[ℛ, 1 / 4]

Visualize the shell:

Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 40]

A Boolean combination of inequalities:

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1 || (0 ≤ x ≤ 1 && 0 ≤ y ≤ 1 && 0 ≤ z ≤ 1) || (x^2 + y^2 ≤ 1 / 9 && -2 ≤ z ≤ 2), {x, y, z}];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

Visualize the shell:

Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 40]

Mesh Regions  (3)

Find the shell of a BoundaryMeshRegion:

Wolfram Language code: ℛ = BoundaryMeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Polygon[{{3, 2, 1}, {2, 3, 4}, {3, 1, 4}, {1, 2, 4}}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

Visualize the shell:

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

MeshRegion:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Tetrahedron[{1, 2, 3, 4}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

Visualize the shell:

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

A closed surface MeshRegion:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Polygon[{{3, 2, 1}, {2, 3, 4}, {3, 1, 4}, {1, 2, 4}}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

Visualize the shell:

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

Applications  (5)

Hollow out a 3D model:

Wolfram Language code: model = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

A torus:

Wolfram Language code: model = ExampleData[{"Geometry3D", "Torus"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

A molecule:

Wolfram Language code: model = ChemicalData["Water", "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

Find a shell with roughly one quarter the original volume:

Wolfram Language code: ℛ = PolyhedronData["Dodecahedron", "BoundaryMeshRegion"];

Sample points in the region to create a distribution of distances to the boundary:

Wolfram Language code: dists = -SignedRegionDistance[ℛ, RandomPoint[ℛ, 2000]];
Wolfram Language code: 𝒟 = SmoothKernelDistribution[dists];

Find the distance where one quarter of the sampled points are closer to the boundary:

Wolfram Language code: t = Quantile[𝒟, 0.25]

The resulting shell:

Wolfram Language code: 𝒮 = BoundaryMeshRegion[ShellRegion[ℛ, t], BaseStyle -> Opacity[0.4]]

Compare the volumes:

Wolfram Language code: Volume[𝒮] / Volume[ℛ]

Use ShellRegion to save material when printing a 3D object:

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {100, 3}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

The shell requires less material:

Wolfram Language code: Volume[𝒮] / Volume[ℛ]

Properties & Relations  (3)

ShellRegion preserves the outer surface of an object:

Wolfram Language code: ℛ = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

Extract the outer surface:

Wolfram Language code: outer = SortBy[ConnectedMeshComponents[RegionBoundary[𝒮]], Area][[-1]]

Compare properties:

Wolfram Language code: RegionBounds[ℛ] == RegionBounds[outer]
Wolfram Language code: Area[RegionBoundary[ℛ]] == Area[outer]

Typically, the thickness of the shell is roughly uniform:

Wolfram Language code: ℛ = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[ℛ, 0.25];

Extract the inner and outer surfaces:

Wolfram Language code: {inner, outer} = SortBy[ConnectedMeshComponents[RegionBoundary[𝒮]], Area]

Compute distances to the outer surface with RegionDistance:

Wolfram Language code: RegionDistance[outer, MeshCoordinates[inner]]//Short

The shell of Ball is SphericalShell:

Wolfram Language code: Graphics3D[{Opacity[0.4], SphericalShell[]}, Boxed -> False]

Use ShellRegion to compute the shell of other regions:

Wolfram Language code: Graphics3D[{Opacity[0.4], ShellRegion[Ball[]]}, Boxed -> False]
Wolfram Language code: Graphics3D[{Opacity[0.4], ShellRegion[Cuboid[]]}, Boxed -> False]

Possible Issues  (2)

The thickness of a shell may not be uniform:

Wolfram Language code: 𝒮 = ShellRegion[ImplicitRegion[x^2 + y^2 - z^3(1 - z) ≤ 0, {x, y, z}], 1 / 10];
Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 100]

Different representations of a region can give different shells:

Wolfram Language code: ShellRegion[Ball[]]

A Ball as an ImplicitRegion:

Wolfram Language code: ShellRegion[ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}]]
Wolfram Research (2016), ShellRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/ShellRegion.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_shellregion, author="Wolfram Research", title="{ShellRegion}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ShellRegion.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_shellregion, organization={Wolfram Research}, title={ShellRegion}, year={2016}, url={https://reference.wolfram.com/language/ref/ShellRegion.html}, note=[Accessed: 12-June-2026]}