The height of the 1x1x1 LEGO brick is 6/5 times its width. Is there any particular reason for these proportions? And especially why not making a cubic brick (it would have made SNOT building easier)?
In the 60s, Lego did produce a separate system for architectural modelling called Modulex which used a 1:1 ratio 5mm cube as its basic brick. It wasn't successful and was discontinued in the late 60s.
I believe the 6:5 was chosen so that studs could fit into the geometry. Related: why the plate is 1/3 of the brick's height. By adding two plates to the height of the brick vertically you can now match the centres of two horizontal units (6+2+2):(5+5)