# 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

open allclose all

## 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: