Do you really need all those flat planes in your dome?

[Christopher Jones]

On page 8 of his Dome Cookbook of Geodesic Geometry, David Kruschke took issue with Domebook 1 and Domebook 2 by Pacific Domes, as they claimed that some domes did not have a level bottom course. His frequency 3 and 4 frequency dome subdivisions address and solve this problem.

His method is overkill, however, if all you want is a 3/8 or 5/8 cutoff of a 4 frequency dome. You only take advantage of 2 out of 3 of the horizontal cutoff planes. The only contribution of the 6 other flat planes resulting from triangular symmetry is to reduce the number of different chord factors.

With help from ChatGPT I have devised a method of subdivision which gives two specified horizontal flat planes but avoids other unnecessary constraints, resulting in a dome with a perhaps more pleasing arrangement of triangular faces. It is also applicable to any frequency of subdivision, whereas the Kruschke method is problematical for frequencies greater than 5.

Here is an example 3D model showing the top 15 spherical triangles of a dome with frequency 15 subdivision. It shows the arcs joining vertices instead of the struts.

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/icosahedral_dome_v15_s3_gnomonic_piecewise.glb

The red arcs are great circles subdivided by radial projections of the linear subdivision of the icosahedral triangular edges.

The green arcs are small circles subdivided by a gnomonic construction based on blue coordinate families.

The blue arcs are continuous great-circle segments from side to green row, across green row, and from green row to side.

[Robert Clark]

Chris,

I'd be interested to know in what way you utilized ChatGPT to reach a solution? That could be really useful.

Robert

[Christopher Jones]

Here are the chord factors for this dome:-

https://chrisjones.id.au/Spherical%20Tessellations/icosahedral_triangle_v15_s3_chord_factors_grouped_v4.pdf

[Levente Likhanecz]

when i'm looking at  flat planes derived domes, it is pleasing. 　
and i have the feeling, maybe it has something with structural strength. 
i really don't understand, that for the sake of uniformity of building elements why to throw away the uniformity of the whole.
those zig-zag line just for 1-2 less strut count, triangular panel count. 
if someone build dome from bricks there may be necessary to avoid flat lines around, to cancel out fracture lines.

On Mon, Jul 27, 2026 at 7:50 AM Christopher Jones <short.jon...@gmail.com> wrote:

Here are the chord factors for this dome:-

https://chrisjones.id.au/Spherical%20Tessellations/icosahedral_triangle_v15_s3_chord_factors_grouped_v4.pdf

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[Christopher Jones]

Robert

ChatGPT is pretty good at coding Python scripts when given clear instructions on what is required.

I had some ideas about spherical subdivision which I asked ChatGPT to implement but the results were not what I expected and not successful. I asked ChatGPT to improve on my suggestions and gave feedback on its proposed scripts until  a good solution was found

Regards

Chris

[Robert Clark]

Chris,

Thank you. I'll have to give it a try one of these days. Last year I tried it out once to have it solve a Pentominoes puzzle. It took more than a few iterations, but eventually it did work. Hadn't thought about having it solve for dome geometry.

Robert