Solution
= Solution
Take
$$
a_1=(-1,1,1)/2,\quad a_2=(1,-1,1)/2,\quad a_3=(1,1,-1)/2.
$$
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
$$
b_1=2π(0,1,1),\quad b_2=2π(1,0,1),\quad b_3=2π(1,1,0).
$$
These generate a face-centred cubic lattice; thus the <reciprocal lattice> of BCC is FCC, with the displayed scale.