A small Miller family gives an exact plane spacing. 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 choose a plane family

The toy cubic cell has side 6 metres. The family uses indices 2, 1, 2.

22+12+22=92^2+1^2+2^2=9
Miller spacingA perfect-square Miller family gives an exact plane spacing.spacingplane family

A perfect square keeps spacing exact

The square sum is 9, so the denominator is 3 and spacing is 2 metres.

6/3=26/3=2
Miller spacingA perfect-square Miller family gives an exact plane spacing.spacingplane family