Icosahedron
represents a regular icosahedron centered at the origin with unit edge length.
Icosahedron[l]
represents an icosahedron with edge length l.
Icosahedron[{θ,ϕ},…]
represents an icosahedron rotated by an angle θ with respect to the z axis and angle ϕ with respect to the y axis.
Icosahedron[{x,y,z},…]
represents an icosahedron centered at {x,y,z}.
Details and Options
- Icosahedron is also known as regular icosahedron.
- Icosahedron can be used as a geometric region and graphics primitive.
- Icosahedron[] is equivalent to Icosahedron[{0,0,0},1].
- Icosahedron[l] is equivalent to Icosahedron[{0,0,0},l].
- CanonicalizePolyhedron can be used to convert an icosahedron to an explicit Polyhedron object.
- Icosahedron can be used in Graphics3D.
- In graphics, the points and edge lengths can be Scaled and Dynamic expressions.
- Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, Texture and color.
- The following options and settings can be used in graphics:
-
VertexColors Automatic vertex colors to be interpolated VertexNormals Automatic effective vertex normals for shading VertexTextureCoordinates None coordinates for textures
Examples
open all close allBasic Examples (3)
Graphics3D[Icosahedron[]]ℛ = Icosahedron[];{Graphics3D[{Pink, ℛ}], Graphics3D[{EdgeForm[Thick], ℛ}], Graphics3D[{EdgeForm[Dashed], ℛ}], Graphics3D[{EdgeForm[Directive[Thick, Dashed, Blue]], Pink, ℛ}]}ℛ = Icosahedron[{1, 2, 3}, 2];Volume[ℛ]RegionCentroid[ℛ]Scope (9)
Graphics (7)
Specification (4)
Graphics3D[Icosahedron[]]A unit icosahedron with explicitly specified edge length:
Graphics3D[Icosahedron[1], PlotRange -> 2]An icosahedron with edge length 2:
Graphics3D[Icosahedron[2], PlotRange -> 2]An icosahedron with edge length 1/2 centered at (1/2, 1/2, 1/2):
Graphics3D[Icosahedron[{1, 1, 1} / 2, 1 / 2], PlotRange -> 1.1]A unit icosahedron rotated by 45° around the 
axis:
Graphics3D[Icosahedron[{45°, 0}], PlotRange -> 1]A unit icosahedron rotated by 45° around the 
axis:
Graphics3D[Icosahedron[{0, 45°}], PlotRange -> 1]An icosahedron of edge length 2 rotated by 45° around the 
axis and 45° around the 
axis:
Graphics3D[Icosahedron[{45°, 45°}, 2], PlotRange -> 2]An icosahedron of edge length 1 centered at (1/2, 1/2, 1/2) rotated by 45° around the 
axis and 45° around the 
axis:
Graphics3D[Icosahedron[{1, 1, 1} / 2, {45°, 45°}, 1], PlotRange -> 2]Styling (3)
FaceForm and EdgeForm can be used to specify the styles of the faces and edges:
ℛ = Icosahedron[];Graphics3D[{EdgeForm[{Thick, Dashed, Blue}], FaceForm[{Pink, Opacity[0.7]}], ℛ}, Boxed -> False]Apply a Texture to the faces:
ℛ = Icosahedron[{0, 0, 0}, VertexTextureCoordinates -> Flatten[Table[{j / 3, i / 2}, {i, 0, 2}, {j, 0, 3}], 1]];Graphics3D[{Texture[[image]], ℛ}, Lighting -> "Neutral"]Assign VertexColors to vertices:
ℛ = Icosahedron[{0, 0, 0}, VertexColors -> ColorData[54, "ColorList"]];Graphics3D[ℛ, Lighting -> "Neutral"]Regions (2)
Embedding dimension is the dimension of the space in which the icosahedron lives:
ℛ = Icosahedron[];RegionEmbeddingDimension[ℛ]Geometric dimension is the dimension of the shape itself:
RegionDimension[ℛ]ℛ = Icosahedron[];BoundedRegionQ[ℛ]r = RegionBounds[ℛ]Graphics3D[{{EdgeForm[White], Opacity[0.2, Yellow], Cuboid@@Transpose[r]}, ℛ},
Boxed -> False]Text
Wolfram Research (2019), Icosahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Icosahedron.html.
CMS
Wolfram Language. 2019. "Icosahedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Icosahedron.html.
APA
Wolfram Language. (2019). Icosahedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Icosahedron.html