# GeodesicPolyhedron

gives the ordern geodesic polyhedron.

GeodesicPolyhedron["poly",n]

gives the ordern 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".
• is effectively equivalent to GeodesicPolyhedron["Icosahedron",n].

# 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_2024_geodesicpolyhedron, author="Wolfram Research", title="{GeodesicPolyhedron}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}", note=[Accessed: 16-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_geodesicpolyhedron, organization={Wolfram Research}, title={GeodesicPolyhedron}, year={2022}, url={https://reference.wolfram.com/language/ref/GeodesicPolyhedron.html}, note=[Accessed: 16-July-2024 ]}