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Edit Mesh / Add Divisions .. will cut a polygonal mesh into uniform squares.

Exponential tessellates by triangular divisions. For example, I’ve tessellated this icosahedral sphere into a round version of the same by going to Edit Mesh / Add Divisions ..

After that, you can triangulate, using Edit Mesh / Add Divisions ..

You can experiment with the settings, but Exponential is the setting you need to add divisions to this type of mesh.

See also Mesh / Smooth.

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