As a kid I figured out the perpendicular connection trick, the height of a “1” tall (flat plate kind of) piece is the same as the width between two pegs, so you can wedge em in there for neat reasonably sturdy perpendicular connections.
Yes, more precisely the elementary unit is the difference between the width and height of a 1x1x1 brick, which is also:
* half the height of a plate.
* the distance between the edge of the brick and the edge of the stud (half the distance between studs)
* one third the diameter of studs
* the height of the studs, except for the LEGO logo (which means that in some cases hollow or recessed studs are very helpful, because an illegal connection can become legal with hollow studs; https://www.bricklink.com/v2/catalog/catalogitem.page?P=8586... is a very useful element in some intricate builds).
The LEGO system is great and everything makes a lot more sense once you figure out that the height of 1 brick and 2 plates is the same as the width of 2 bricks. For example I made a car where the sides are built "front to back" and attached sideways to the chassis (https://rebrickable.com/mocs/MOC-7455/bonzinip/awd-champions...).
In addition, the inside diameter of hollow studs is
the same as the diameter of clips and minifigure hands, and the same as the inside diameter of Technic pegs. There are a lot of newer parts that use this "secondary" system, but the basic measurements were established in the 70s. See http://www.newelementary.com/2016/12/bravo-three-one-eight.h... for more information.
(A standard brick is 3 tall, in this calculus)