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The fluorite structure consists of a face-centered cubic lattice of calcium sites with all eight tetrahedral interstitial sites occupied by fluoride. In fractional coordinates of the conventional cubic unit cell, the calcium basis is $(0,0,0),(0,\frac{1}{2},\frac{1}{2}),(\frac{1}{2},0,\frac{1}{2}),(\frac{1}{2},\frac{1}{2},0)$, and fluoride occupies all combinations $(x,y,z)$ with $x,y,z\in \{\frac{1}{4},\frac{3}{4}\}$. The projection therefore superposes two fluoride sites at each quarter-coordinate position. Labels in the original diagram give fractional depth along $[001]$; periodic boundary sites are displayed on both edges.

Counting shared sites gives $8/8+6/2=4$ calcium sites and eight interior fluoride sites: four formula units per conventional cell.

Each calcium cation has eight fluoride neighbours at the vertices of a cube: cubic coordination. Each fluoride anion has four calcium neighbours in tetrahedral coordination. Both unlike-neighbour Euclidean distances are $\sqrt{3}a/4$, with $a$ the conventional cubic lattice parameter.

Apply the Goldschmidt packing principle at its limiting eight-coordinate geometry: the eight surrounding anions just touch one another and also touch the central cation. The anions form a cube of edge $a/2$, so $2r_a=a/2$ and $r_a+r_c=\sqrt{3}a/4$. Eliminating $a$ givesEquivalently, $r_c/r_a=0.732$. This is a limiting radius ratio rule, rather than a measured ionic-radius ratio. It does not assume that the calcium sublattice consists of mutually touching spheres: the calcium positions have face-centred cubic symmetry, but that symmetry alone does not specify which ions touch. A different construction with touching calcium spheres and fluoride just filling their tetrahedral interstitial sites would instead give $r_a/r_c=\sqrt{3/2}-1=0.225$; that is the opposite contact limit, not the eight-coordinate anion-contact ideal used here.