What is the base mesh / skeleton of this shape?

Hello,

I am analyzing the geometry of the lampshade pattern below. I am not looking for a step-by-step tutorial or a complete Grasshopper definition, but rather a discussion on the fundamental base shape and the underlying skeleton of the texture.

My current thought is that the base shape is simply a flared surface of revolution (bell shape). The skeleton seems to be a standard UV quad grid where the vertices are displaced along the surface normals in a staggered/checkerboard pattern to create the scales and gaps.

Is this the most logical base topology for this kind of structure, or is there a different underlying geometric framework driving this specific pattern?

Looking forward to hearing your insights on the core logic.

I remember similar stuff popping up when searching for “surface gills” or “zig zag ribbons”

I believe it is something like this:

A hex panelization with that sort of cell topology. There might be some more bevels to achieve the exact result, but I think this might be a good starting point.

See attached definition, I used LunchBox and froGH to speed up hex and mesh generation. I did it focusing on the cell geometry, so I did not bother doing a properly closed hex panelization.
hex mesh lamp.gh (44.0 KB)

Thank you very much, @ale2x72
I guess your method is the right way. I will go deeper with this idea. I will post the result if I have the right one.

Thank you very much, I will search them.

六角檐灯罩 v0.gh (226.2 KB)
Created from @ale2x72’s concept: morph unit patterns into hex polygons.

But the lamp shade in the image was not designed with morphing unit pattern method, because that is a clay print, which requires every colored layer to have exactly the same height. I managed to find the right way.

Wut? A clay print generally has more leeway than, say, a plastics print because the layers are much thicker.