GeodesicPolyhedron

GeodesicPolyhedron[n]

gives the order‐n geodesic polyhedron.

GeodesicPolyhedron["poly",n]

gives the order‐n geodesic polyhedron based on the polyhedron "poly".

Details and Options

Examples

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Basic Examples  (1)

Generate a geodesic polyhedron:

Compute the volume:

Scope  (6)

Basic Uses  (5)

Generate an equilateral tetrahedron, octahedron, icosahedron, etc.:

Color directives specify the face colors of geodesic polyhedrons:

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

Geodesic polyhedra are three-dimensional geometric regions:

Geometric dimension:

Find the geometric properties of a geodesic polyhedron:

Surface area:

Specifications  (1)

A geodesic polyhedron can be specified by its standard Wolfram Language name:

Applications  (2)

Generate a gallery of geodesic polyhedron:

Generate the duals of a gallery of geodesic polyhedron:

Properties & Relations  (5)

A geodesic polyhedron is convex:

A geodesic polyhedron is simple:

The OuterPolyhedron of a geodesic polyhedron is itself:

Geodesic polyhedrons do not have holes:

The number of faces of a geodesic polyhedron from Icosahedron:

The formula:

The number of vertices of a geodesic polyhedron from Icosahedron:

The formula:

Wolfram Research (2022), GeodesicPolyhedron, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html.

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_2025_geodesicpolyhedron, author="Wolfram Research", title="{GeodesicPolyhedron}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geodesicpolyhedron, organization={Wolfram Research}, title={GeodesicPolyhedron}, year={2022}, url={https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}, note=[Accessed: 21-February-2025 ]}