Triangles are also a very good way to store data. If you boil it down to just geometry, then to draw a triangle you need to store 3 points in 3D space (the most memory) then the order that the edges connect. To draw the NEXT triangle you only need to store one other 3D point, since 2 points already exist. What you end up doing then is usually storing a point list, and some data to describe how to turn those into a surface.
It gets more complicated after that, not all triangles are connected, you are storing directional normal for each point, texcoords and so on…
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