A plane-family spacing is a checked geometry ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Miller indices define the training family
The family is indexed by 2, 2, and 1. The squared denominator is 9.
h2+k2+l2=9
The plane spacing is forced by geometry
With lattice constant 12 m, the exact spacing is 4 m. This is schematic indexing, not structure refinement.