All I need is a way to extrude an object through script, but by adding vertices and faces.

I can explain it easier through this Blender photo:

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So instead of just changing the objects scale, I want to add on extra faces/vertices. Is there an easy way to accomplish this? (I use C# by the way)

Look at the Mesh class: Mesh.

What you need to do, is add vertices and triangles to the mesh.

I believe that the unity cube is made out of 24 vertices (3 in each corner) and 12 triangles (2 on each “face”).