Creating a planar diamond mesh on the ribbon

Hello Guys

tell me please, is it possible to somehow put a mesh in the form of rhombuses on the form in the form of a ribbon, so that it is flat?
I get that it becomes square when deformed to planarity?

planar diamond mesh.3dm (1.1 MB)
planar quad mesh.gh (898.7 KB)

Hi @AlexWer

For the mesh quads to be flat (and stay connected to each other and on the surface), they’d need to follow the curvature of the surface. So yes - they’d become approximately rectangles (strictly isosceles trapezoids, with top and bottom horizontal) on this surface of revolution.
When a quad is oriented diagonal to the surface curvature, that quad is non planar.
curvature_00001

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David, thanks a lot for your reply.

As I understand it, on surfaces with negative Gaussian curvature, it is mathematically impossible to put squares at an angle in a planar way.