Grasshopper

algorithmic modeling for Rhino

I have a problem with generating a geodesic dome. Why are the hexagons in this model not planar? Maybe it's mathematical impossible? Or?

Geo_Dome_2.gh [this file uses WB components]

I hope somebody can clear this up for me, and help me be able to generate planar surfaces in the hexagons.

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Hi.

How about using Kangaroo2 for planarization?

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I see your point, but it was quite not the solution I was looking for, it's a bit too hax, the math need add up.

I don't know why it does initially work..

But then I look here:
http://mathworld.wolfram.com/GeodesicDome.html

In such domes, neither the polyhedron vertices nor the centers of faces necessarily lie at exactly the same distances from the center. However, these conditions are approximately satisfied.

So maybe it's not possible to generate such a thing? But then again how is it done in this component ? [Example1.png]

But then again again I look at the amount of different line lengths in the exploded hexagons from that example and note there are some inconsistencies. [example2.png]

Conclusion:
Wolfram Alpha is correct, it's not possible to generate this shape without 'haxing' around with the points to make it fit planar surfaces.

But it should be possible to generate an approximation that is good enough, actually the method presented by Hyungsoo Kim should be just as fine as anything else.

Thank you!

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Maybe it depends on the method you use to generate the dome?

I thought geodesic domes start as an icosohedron... 20 equilateral triangles with all vertices lying on a sphere.

Divide the equilateral triangles into more triangles and project the points of these triangles onto the sphere.

The more triangles you divide the original equilateral triangles into, the closer to a sphere you get but the more variation in length of triangle edge and corner node geometry.

This method is also giving you triangles not hexagons and pentagons, but you can see the hexagons and pentagons made up of the triangles.

How about using the facet dome component like this?:

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