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I was poking around in a cycles material test scene which I donwloaded, and when I looked at the mesh for the sphere, it looked like this:

Strange mesh pattern This looks nothing like either the UV sphere or the ICO sphere, so what function would transform the mesh into something like this?

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There's no function to create meshes except for pre-made ones (primitives like what's in Shift+A menu, etc.) You should add a primitive and know how to edit it in order to get result you'd like to. – Mr Zak Mar 26 at 21:11
up vote 6 down vote accepted

This is a subdivided icosphere, generated from a basic icosphere via a subdivision surface modifier.

enter image description here

Of course the blender logo was then carved out of it via a boolean modifier.

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Aha, I feel like an idiot for not noticing that earlier. – Hexatin Mar 26 at 21:12
    
Happens to me all the time :) – TLousky Mar 26 at 21:13

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