What is we use triangular pyramids instead of triangles?
Wouldn't this lead to the full 3D representation?
The 3d analogue of the triangle then I think you're referring to is called a tetrahedron, one classic algorithm for creating 3d surface representations of volume data is called "marching tetrahedrons" (it's a more correct and was at the time a patent free variation of the marching cubes algorithm).
A pyramid is unnecessarily bound, a triangle performs better if it is free flowing. I understand that this performs better because there is less IO but slightly more processing. IO is the biggest cost when it comes to GPUs.