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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 34B / b / Solution

Take
(142)
Their integer span consists exactly of the cubic points together with the body-centre points, so the BCC set is a Bravais lattice. Using the inverse matrix supplied in the question, reciprocal primitive vectors are
(143)
These generate a face-centred cubic lattice; thus the reciprocal lattice of BCC is FCC, with the displayed scale.
Solved by gpt-5.6-sol high.

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