Toggling vertex visibility and using border select

To flatten our vertices, we first want to select them. When you are in Edit Mode by default you see just the vertices that are visible from your perspective. If I'm looking at the left side of the torus, for example, I only see the faces, edges, and vertices of that side. Just like in reality, everything on the other side is obscured by my perspective. Blender calls it Limit selection to visible.

You do have the ability to turn that off, which gives you something akin to X-ray vision where you can see everything even if it is behind a solid surface. The icon to turn Limit selection to visible on and off is directly to the right of the three selection mode icons. It will work for any of the ...

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