In textbooks, an intrinsic (=pure) semiconductor crystal is always drawn as a two-dimensional grid of neatly arranged atoms (usually Si or Ge) with 4 valence electrons each, forming covalent bonds with 1 electron each of its 4 neighbouring atoms, giving 8 valence electrons in the outer shell. But in practice, the crystals are three-dimensional, so each atom has 6 neighbours instead of 4.
So why do we always draw them as 2-D structures? Why can we make this simplification? What would change if we did not do this simplification? How would that impact the analysis of the semiconductor devices? What would change in the formulas we derive?