Subdivided Geodesic Dodecahedron?

Following up on this post from 2011 on the old forums, Gabe Krause was paneling a dome with circles.

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Which was VERY cool (aside from minor cheating with ovals) but I’m very interested in the geodesic dodecahedron he created in the process.

Normally geodesic domes are bisected awkwardly at the center, this is really nice! His definition, cutting edge for 2011 perhaps, is very dense, isn’t using any modern plugins, and is devoted largely toward the circle/oval endeavor.

Does anyone know how I could take a stab at this more efficiently today? I can bring in a Dodecahedron either through Polyhedra or Weaverbird but I don’t quite understand the subdivision/frequency process, I’m not accustomed to subdividing with more faceted results, assuming I am understanding how this is happening. I just ordered a book on geodesic math so if nothing else maybe I can figure it out on my own and report back.

Attached is the original definition by Gabe, and empty canvas with a Dodecahedron.

GeodesicDomePaneling by Gabe.ghx (4.1 MB)

interalized dodecahedron.gh (4.2 KB)

Talking about subdivision wouldn’t something like this do it? (I mean the image) Just subd a icosahedron with Weaverbird. Or do you want to implement the subdivision yourself? Or I am missing something.

If you just want the triangles, you can subdivide and project with Weaverbird like this:
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If you do want a tangent circle packing you can do it like this


sphere_circlepack.gh (18.4 KB)

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Out of interest… is this geodesic dome better from a manufacturing point of view or just aesthetic? I’m not sure what you mean by the “bisected awkwardly”?

@martynjhogg Where a sphere is cut in half to become a dome, in most of the geodesics I’ve been playing with faces are being cut at the bottom.

In the case of the Dodecahedron I shared earlier, and the Icosahedron @DanielPiker shared, there is a perfect separation point between hemispheres. To be honest though, the geodesic Dodecahedron and Icosahedron are essentially the same. I don’t know if the original file I found was mislabeled or I’m not understanding geodesic math, most likely the latter.

Structurally, all of these are more than suitable I assume, at least in the tests I’m running, so it’s more of an ascetics thing. We’re building one traditional geodesic dome and one circle packing dome at work.

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The one in your image looks like it also has a planar equator, it just needs orienting differently.
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@DanielPiker If I remember correctly, I was meeting higher than the planar equator. Thank for you for the circle packing, very cool alternative the load/collisions.

I’m still comparing the old “Dodecahedron” with the Icosahedron you shared, do you know why the Icosahedron isn’t getting better symmetry?

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Is this from the circle packing optimization definition above?
The circle packing energy does allow Möbius transformations, so that might be what you are seeing.


It should be possible to avoid these transformations though by simply anchoring the top point in X and Y.

I’ve done geodesic domes before by starting with an icosohedron ans splitting the triangular faces, then projecting the new triangle vertices out onto the original sphere that all the points of the icosohedron lie on.

The more you divide the original icosohedron faces, the higher the resolution of the dome and the closer it is to representing a sphere.

Presumably, you are doing the same with a regular dodecahedron but splitting the pentagons into 5 triangles and projecting these new vertices onto the original sphere?

That’s the idea, not doing a great job of getting symmetry though. I ended up downloading Cadre Geo, a software for generating very precise geodesic structures, I’m trying to duplicate this feature in grasshopper now, counting unique segments, hubs and surfaces.

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Wondering if there is a component like Remove Duplicate Curves but for finding the index of duplicate lengths rather than positions.

A big issue with creating more ambitious structures is the amount of unique parts skyrocket, need to find a balance.

You can use RhinoPolyhedra

polyhedra.gh (10.3 KB)

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Okay, Set Union was my huckleberry for finding duplicate data but it doesn’t give me the index of duplicate data, which would be helpful for construction drawings. One of my goals is to label and highlight the different duplicate (or close enough) components.

In this case, out of 250 struts we have 6 unique lengths.

dome break down.gh (82.5 KB)

@seghierkhaled Thanks! Digging into that now.

@seghierkhaled Is it a crapshoot trying to rotate these to find an equator line to divide these symmetrically into domes? Each is going to be so unique, I’m assuming it’s more of a bake, explode, orient and bring back into gh maneuver?

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I am not sure if this have an equator line

Often they split the domes above or below the actual equator because there is a flatter split line there. Then the dome is built on a plinth which takes up any out of flatness.

SNOWDONDOMES

See the gallery on this page. You can see the smaller, lower frequency domes are split below the equator giving just over a hemisphere and the larger, higher frequency domes are split above the equator giving just less than a hemisphere.

If you try and split them exactly on an equator then you just get loads more unique struts and nodes.

I never found a way of automatically finding the split line so you are probably right to bake the full dome, split it manually and then import it again until some genius works out a way to use Lunchbox’s Machine Learning components or something to do it for you :slight_smile:

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