I'd like answers both in the more intuitive side an on the more precise side. 

Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?

I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ?