Confused by vertexes and surfaces

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The order matters because the order, clockwise, or counterclockwise, tells the 3D card which way the front of the triangle is pointing.

Normally, only triangles which are facing the camera are drawn. This makes rendering go faster, because triangles which face away from the camera are almost always hidden completely behind triangles which face towards the camera, unless your object has missing polygons.

So it's for speed.

And it's for other stuff too, but that has to do with a lot of complicated math you don't need to worry about.