gives the order‐n geodesic polyhedron.
GeodesicPolyhedron ["poly",n]
gives the order‐n geodesic polyhedron based on the polyhedron "poly".
GeodesicPolyhedron
gives the order‐n geodesic polyhedron.
GeodesicPolyhedron ["poly",n]
gives the order‐n geodesic polyhedron based on the polyhedron "poly".
Details and Options
- GeodesicPolyhedron is also known as icosphere.
- GeodesicPolyhedron is typically used to approximate a sphere.
- GeodesicPolyhedron ["poly",n] gives a Polyhedron generated by subdividing faces of "poly" and projecting the new points onto the surface of the unit sphere.
- Possible values of "poly" include "Tetrahedron", "Octahedron" and "Icosahedron".
- GeodesicPolyhedron [n] is effectively equivalent to GeodesicPolyhedron ["Icosahedron",n].
- GeodesicPolyhedron takes the following options:
-
Examples
open all close allBasic Examples (1)
Generate a geodesic polyhedron:
𝒫 = GeodesicPolyhedron[3]Region[%]Compute the volume:
Volume [𝒫]Scope (6)
Basic Uses (5)
Generate an equilateral tetrahedron, octahedron, icosahedron, etc.:
Table[Graphics3D[GeodesicPolyhedron[name, 1]], {name, {"Tetrahedron", "Octahedron", "Icosahedron"}}]Color directives specify the face colors of geodesic polyhedrons:
Table[Graphics3D[{c, GeodesicPolyhedron[2]}], {c, {Red, Green, Blue, Yellow}}]FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:
Graphics3D[{FaceForm[Pink], EdgeForm[Directive[Dashed, Thick, Blue]], GeodesicPolyhedron[2]}]Geodesic polyhedra are three-dimensional geometric regions:
RegionQ[GeodesicPolyhedron[2]]Geometric dimension:
RegionDimension[GeodesicPolyhedron[2]]Find the geometric properties of a geodesic polyhedron:
Volume[GeodesicPolyhedron[2]]Surface area:
SurfaceArea[GeodesicPolyhedron[2]]Specifications (1)
A geodesic polyhedron can be specified by its standard Wolfram Language name:
GeodesicPolyhedron["Tetrahedron", 2]Graphics3D[%]Applications (2)
Generate a gallery of geodesic polyhedron:
Grid[Table[Graphics3D[GeodesicPolyhedron[name, i], Boxed -> False], {name, {"Tetrahedron", "Octahedron", "Icosahedron"}}, {i, 4}]]Generate the duals of a gallery of geodesic polyhedron:
Grid[Table[Graphics3D[DualPolyhedron[GeodesicPolyhedron[name, i]], Boxed -> False], {name, {"Tetrahedron", "Octahedron", "Icosahedron"}}, {i, 4}]]Properties & Relations (5)
A geodesic polyhedron is convex:
GeodesicPolyhedron[2]ConvexPolyhedronQ[%]A geodesic polyhedron is simple:
GeodesicPolyhedron[2]SimplePolyhedronQ[%]The OuterPolyhedron of a geodesic polyhedron is itself:
𝒫 = GeodesicPolyhedron[2]OuterPolyhedron[𝒫]Geodesic polyhedrons do not have holes:
InnerPolyhedron[𝒫]The number of faces of a geodesic polyhedron from Icosahedron :
Table[Length[GeodesicPolyhedron["Icosahedron", n][[2]]], {n, 5}]The formula:
FindSequenceFunction[%, n]The number of vertices of a geodesic polyhedron from Icosahedron :
Table[Length[PolyhedronCoordinates@GeodesicPolyhedron["Icosahedron", n]], {n, 5}]The formula:
FindSequenceFunction[%, n]History
Text
Wolfram Research (2022), GeodesicPolyhedron, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html.
CMS
Wolfram Language. 2022. "GeodesicPolyhedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html.
APA
Wolfram Language. (2022). GeodesicPolyhedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html
BibTeX
@misc{reference.wolfram_2026_geodesicpolyhedron, author="Wolfram Research", title="{GeodesicPolyhedron}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}", note=[Accessed: 05-September-2026]}
BibLaTeX
@online{reference.wolfram_2026_geodesicpolyhedron, organization={Wolfram Research}, title={GeodesicPolyhedron}, year={2022}, url={https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}, note=[Accessed: 05-September-2026]}