80 vertices in 2-fold dihedral symmetry has triangle strips of 4 different lengths.
We can also get 80-vertex tetrahedral symmetry with a more "traditional" arrangement of 12 pentagons and the rest hexagons.
Here is an 80-vertex sphere in tetrahedral symmetry with 24 valence-7 vertices.
✨ I just made a new release of ShaderWorkshop¹ (v0.5.0).
Since my last release announcement, quite a few features got added (about 2 releases):
- recursive include directive
- fps indicator
- reworked error management
- mouse support
- live controls for floats, int, bool and colors
No More Shading Languages: Compiling C++ to Vulkan Shaders
I can't compete with the mod or fract version in term of code length, but I'm able to get the HSL and HSV conversions without any of these functions, so I guess it's faster?
mod version is derived from iq, fract version derived from @samhocevar, and the clumsy arithmetic from me.
Can we do better?
Tetrahedral symmetry requires that a general point be in a set of 12 -- on each of the 4 faces in each of 3 orientations. You can also add 4 points at the vertices, 4 at each face center, or 6 at each edge center. Combined, any even number of points >= 4 can be arranged with tetrahedral symmetry, albeit not always evenly.
Here is 50 points in tetrahedral symmetry which requires that some of them have valence 7.
I've been porting https://github.com/2Retr0/GodotOceanWaves to the Recoil Engine/Beyond All Reason. Need to do a bit of work on optimization, a ton of clean up, and then adding some features.
My fish schooling sim(boids) needed a nicer place to live. So I went to work.
Pretty far from done but there is potential.
testing new wrinkle system on torso.
ultra fast fbm : )
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50 vertices arranged in D6 symmetry is interesting in that it forms two different but close in length triangle strips -- one following the longitudes and the other the latitudes.
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And 22 vertices can also arrange with 2-fold cylindrical symmetry that runs all the pentagons together into one long strip. It produces one long triangle strip and three short ones.
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22 vertices can also arrange with 2-fold dihedral symmetry with two strips of six pentagons each separated by a single loop of 10 hexagons. The triangulation has two long triangle strips and two short ones.
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40 vertices in tetrahedral symmetry gives a mix of the two with 4 strips that wrap twice and three that only wrap once.
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22 vertices can also have tetrahedral symmetry, but now only have four strips that each wrap the sphere twice.
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16 vertices gives a triangulation with tetrahedral symmetry. It has 7 triangle strips.
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In contrast, the 12-vertex icosahedron has 6 triangle strips.
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