poly_kscope for tetrahedral geospheres

[Gerry in Quebec]

Hi Adrian, Roger & others,

It's been a while since I posted here. I hope you are all thriving.

Here's my question: How do I use poly_kscope to generate a tetrahedral geodesic sphere from one of the clusters of triangles making up one face a tetrahedron? I did check out the Antiprism website for info on that program, but couldn't get it to work. When I do it for geospheres based on the icosahedron and octahedron, there is no problem.

 So here's an example of an off file for one of the four tetrahedral triangle clusters. In this case it's 2-frequenency, so 4 triangles.

OFF      
7 4 0  
0 0 0  
0 0 1  
0.816497 0 0.57735  
-0.40825 0.707107 0.57735  
0.942809 0 -0.33333  
0.408232 0.707078 -0.5774  
-0.4714 0.816497 -0.33333  
3 1 2 3
3 2 4 5
3 3 6 5
3 2 3 5

 And here's what the 2-frequency tetrahedral cluster of 4 triangles looks like:

Thanks for any help with this.

- Gerry in Québec

[Adrian Rossiter]

Hi Gerry

On Fri, 17 Jul 2026, Gerry in Quebec wrote:
> Here's my question: How do I use poly_kscope to generate a tetrahedral
> geodesic sphere from one of the clusters of triangles making up one face a
> tetrahedron? I did check out the Antiprism website for info on that
> program, but couldn't get it to work. When I do it for geospheres based on
> the icosahedron and octahedron, there is no problem.
>
> So here's an example of an off file for one of the four tetrahedral
> triangle clusters. In this case it's 2-frequenency, so 4 triangles.

When you have a component that you want to repeat symmetrically with
poly_kscope then it has to be aligned correctly first. In this case
the component would be aligned with a face of the Antiprism 'tet'
model (at any scale).

I have called your component tet_tris.off. You can see it is not
aligned with 'tet'

antiview tet tet_tris.off

It appears that you have constructed it in a "pyramid" alignment

antiview pyr3 tet_tris.off

In which case, the following command will realign the 3-fold axis of
the component with a 3-fold axis of the 'tet' model (by rotation only),
and you can then repeat it with poly_kscope

off_trans tet_tris.off -Y tet,C3 | poly_kscope -s T | antiview

The original coordinates are low precision, so the repeated vertices
in the final model don't merge well with off_util -M a.

As an alternative. create your model from a couple of key vertices (I
specified them at scale three, then scaled them down afterwards, for
clarity), then repeat them as before and create the convex hull

off_util -A v,0,0,3 -A v,rt6,0,rt3 null | off_trans -S 1/3 | off_trans -Y tet,C3 | poly_kscope -s T | conv_hull | antiview

Adrian.
--
Adrian Rossiter - adr...@antiprism.com
http://www.instagram.com/adrian_rossiter
http://antiprism.com/adrian

[Gerry in Quebec]

Hi Adrian,

Great! Thanks so much for the clear explanation & options.

- Gerry in Québec