Tessellations on a sphere

[kenzan]

TIA to anyone who can help.

Ultimately, I’m trying to make this:

Floret Tessellation of a Sphere

Inside each pentagon, I would like to insert an indentation using some sort of mesh. Something I learned how to do from this video: Beijing Water Cube (Grasshopper Tutorial) - YouTube

If you read the responses from Link 1 above, you can cut a triangle through multiples of this shape and apply them to the faces of an icosahedron. If you look at example 1 in the expression attached, I did apply this group of curves to one face successfully.

BUT, When I input the whole list of faces from the DeBrep to the Trimap, it puts a single curve on each, as in example 2 in the expression. Clearly I could use List item to pull each face, then Trimap to each face, but that seems like something GH should do if asked correctly.

I also know that this is not on a sphere yet, and I have not figured out how to get this all onto a sphere yet. Also I know that I have to slave the size of the pentagons to the size

Finally, if anyone knows how to get a mesh mapped onto the surface of the sphere, I would be very appreciated as well.

Thanks

Flower star Help.gh (22.2 KB)

[martinsiegrist]

In your example you basically just need to graft the T input so the mapping happens on all triangles.

However. Not sure how you’d want to go ahead and join the segments…

The Polyhedra plugin might provide a better starting point. I used a Mesh IcoSphere in the file below.

Instead of mapping line segments, you can also map closedd polylines. The result of that is a mesh with a lot of naked edges. Everything overhanging the triangle needs to be aligned. You need to figure out the tolerance.

The face boundaries can be pulled to a sphere. If you want to split the sphere surface, you will need to clean up the triangles along the seam.

Multipiping the curves is easy. You just need to delete the duplicates.

flower_star_mrtn.gh (24.1 KB)

[kenzan]

Well that certainly skipped a lot of steps. The shape I was looking to make is in there already.

I will start working on this. Thanks so much.

[martinsiegrist]

I edited the post. Check again

[kenzan]

Thank you, I will look.