How to project a pattern on a hemisphere without changing length

Grasshopper
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1

Hello guys.
I need your help with handling grashoppers well!!!

I want to wrap this pattern to hemisphere Dome…
It’s very easy and simple with projection, but all I want is “all curves should be the same length”.
Because i want to make reciprocal frame Dome with this Davinci’s pattern.

화면 캡처 2025-10-11 210141
화면 캡처 2025-10-11 210141674×638 42.1 KB

After talking with ChatGPT, Maybe this is possible through kangaroos.
But I have so little knowledge that it’s hard to solve on my own…
I’ve tried all of the reciprocal tools in Ngon, but I don’t think they’re supposed to make patterns and apply them. Just repeating triangles, squares, hexagons.

plz help me!

2

Reciprocal - Grasshopper / Kangaroo - McNeel Forum

This topic could be helpful

3

Could you share you 3dm or GH file here? Thank you.

4

You’ll find it’s impossible. There is no mapping of a sphere to a plane that preserves length. Reciprocal domes are possible, but the members are all different lengths.

5

I’m working hard on making a grashopper right now. I’ll share the file here once it’s organized to some extent and ask questions!

6

You will probably need to change twelve of the hexagons into pentagons.