Goldberg Polyhedra Pattern on Ellipsoid

Grasshopper
1

Hi,

I’m new to the topics of polyhedras.
I’m trying to apply a Goldberg Polyherdra Pattern onto a given ellipsoid.

Is that possible? I’ve googled around for some solutions
However, most solutions seem to provide a given polyhedra.
I would like a solution that references my geometry and allow me to change the scale and subdivisions.

Can anyone guide me?

2

I have no idea what a “Goldberg Polyherdra Pattern” is so an image would help, perhaps a link that explains it. And as always, post your own GH file with some geometry.

3

These are Goldberg polyhedron:

image
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– Dale

4

More or less easy with code (Level:mid to expert) … rather impossible without (unless there’s some add-on around that does that).

Anyway some quidelines:

  1. First you should do some Geo Dome (shown: a Spherical, Icosahedron, Class I, Frequency 10):

Screen Shot 110
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Obviously you can “distort” in x/y/z and get an Ellipsoid Dome.
Screen Shot 112
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  1. Domes are done in Mesh “format” mostly for speed (Point3f etc) AND for the 6 handy connectivity Methods available in RhinoCommon for the Mesh Class. These connect TopologyVertices, TopologyEdges and Faces via DataTrees of type int.
  2. Then is a matter of connectivity (and MTV Sort as found in the TopologyVertices related Method). Since the Mesh is derivant - in most of cases - from some seed Platonic solid (Frequency is the subdivision) … one can easily mastermind hex patterns (provited that he knows how these Geo Dome Faces are made).

Screen Shot 111
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4. That said most Geo Dome (as Meshes) Vertices have valence 6 meaning that hexagons (and some pentagons) are a given as well in, say, W type of trusses like this one captured (see the black top struts):
Screen Shot 113
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BTW: for the logic of subdivisions (thus the logic of patterns) see this as well: