There's a really obvious **geometric** reason why the cosine of the bond angle in graphite is $-1/2$: the stuff consists of sheets shaped like honeycombs.

There's also a really obvious **geometric** reason why the cosine of the bond angle in methane is $-1/3$: four hydrogen atoms are arranged in a symmetric way about a center, with all six angles between them equal: tetrahedral symmetry.

Is there a **geometric** reason why the cosine of the bond angle in water is $-1/4$?

(I suspect chemists might dismiss this question as being about magic and voodoo and mystical and the like. Mathematicians don't mind magic and voodoo and mysticism, but maybe they object to vagueness or chemistry. So we'll see if this question is tolerated here.)

(Full disclosure: once upon a time I posted nearly this same question somewhere else.....)