The angle 137.5 is related to the golden ratio and gives a close packing of florets.
The fluorine atoms are arranged in the hexagonal close packing.
A typical good value for spherical grains is 0.64, as given by random close packing.
In close packing all of the spheres share a common radius, r. Therefore two centers would simply have a distance 2r.
This relatively close packing leads to a high density of 5.73 g/cm.
It was warm there, because of the close packing of bodies and many breaths.
On raising temperature, the lowest free energy arrangement becomes cubic close packing and then liquid.
Under pressure the lowest energy structure switches between cubic and hexagonal close packing.
This type of crystal structure is known as cubic close packing (ccp).
It is pretty close packing, but we don't stand upon ceremony here.