Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 GeodesateMesh

Source Notebook

Generate a geodesic dome from a polyhedral base

Contributed by: Wolfram Staff

ResourceFunction["GeodesateMesh"][reg,n]

generates a region representing the projection of the order-n regular tessellation of each face of the polyhedron reg onto the circumscribed sphere centered at the origin.

ResourceFunction["GeodesateMesh"][reg,n,p,r]

uses a circumscribed sphere centered at the point p with radius r.

Details

ResourceFunction["GeodesateMesh"][reg] is equivalent to ResourceFunction["GeodesateMesh"][reg,2].
ResourceFunction["GeodesateMesh"] returns a BoundaryMeshRegion object if reg is a BoundaryMeshRegion or Polyhedron object.
ResourceFunction["GeodesateMesh"] returns a GraphicsComplex object if reg is also a GraphicsComplex object.
ResourceFunction["GeodesateMesh"] triangulates polygons with five or more sides before projecting them onto the circumscribed sphere.

Examples

Basic Examples (1) 

Geodesate an icosahedron:

In[1]:=
ResourceFunction["GeodesateMesh"][Icosahedron[], 3]
Out[1]=

Scope (3) 

Use the default geodesation order:

In[2]:=
ResourceFunction["GeodesateMesh"][ PolyhedronData["PentakisDodecahedron", "BoundaryMeshRegion"]]
Out[2]=

Use a different center and radius for the circumscribing sphere:

In[3]:=
ResourceFunction["GeodesateMesh"][ PolyhedronData["TetrakisHexahedron", "BoundaryMeshRegion"], 2, {1/8, 0, 0}, 9/10]
Out[3]=

Use GeodesateMesh on a GraphicsComplex object:

In[4]:=
Graphics3D[ ResourceFunction["GeodesateMesh"][ PolyhedronData["ElongatedTriangularGyrobicupola", "GraphicsComplex"], 3]]
Out[4]=

Properties and Relations (1) 

Use CanonicalizePolyhedron to get a Polyhedron object that can be used in Graphics3D:

In[5]:=
CanonicalizePolyhedron[ ResourceFunction["GeodesateMesh"][ BeveledPolyhedron[Dodecahedron[]]]] // Graphics3D
Out[5]=

Neat Examples (1) 

Visualize a Goldberg polyhedron:

In[6]:=
DualPolyhedron[ CanonicalizePolyhedron[ ResourceFunction["GeodesateMesh"][ PolyhedronData["PentakisDodecahedron", "BoundaryMeshRegion"], 3]]] // Graphics3D
Out[6]=

Version History

  • 1.0.0 – 28 June 2021

Related Resources

Author Notes

GeodesateMesh can return unexpected results if the non-triangular faces of a given polyhedron have been triangulated in advance. If using PolyhedronData, stick to the results of the "BoundaryMeshRegion" or "GraphicsComplex" properties.

License Information