How to create equilateral triangle on a Sphere

How to create paneling grid on a sphere for the construction of a equilateral triangle on a Sphere.

Have you looked at the Polyhedra plugin yet?

I think you could use a Geodesic Icosahedron.

I wanted to find a sphere made up by triangles with same shape and area. However, I couldn’t get it.

A sphere has the minimum surface area for a given volume. Any other shape will have a larger surface area for the same volume.

If I want to prepare cladding panels with one size only to fill the sphere. Is it possible by your plug-in program?

Yes it can be done with that plugin. But there are just a two options:
Hope it helps.

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There’s a limit … known to pythagoras thousands of years ago: There is only a small number of regular polyhedra. The icosahedron is the best you can do.

The work of Alain Lobel is highly relevant here. You might also consider implementing a constraint solver for this. Kangaroo2 and ShapeOp comes to mind. Both available for Rhino/Grasshopper.

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