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Take a primitive real lattice
(11 0)
(2 1 0)
(0 3 0)
(1 0 0)
(2 2 0)
(0 1 0)
(1 1 0)
(1 2 0)
(0 0 0)
(1 2 0)
(1 1 0)
(1 1 0)
(3 3 0)
(1 0 0)
(0 3 0)
(2 1 0)
(1 1 0)
This is the conventional reciprocal unit cell
If the real structure changes such that ...
(22
0)
(21
0)
(2 0 0)
(2 1 0)
(2 2 0)
(12
0)
(11
0)
(1 0 0)
(1 1 0)
(1 2 0)
(0 2 0)
(0 1 0)
(0 0 0)
(0 1 0)
(0 2 0)
(1 2 0)
(1 1 0)
(1 0 0)
(1 1 0)
(1 2 0)
(2 2 0)
(2 1 0)
(2 0 0)
(2 1 0)
(2 2 0)
The new reciprocal unit cell is defined by the shortest real
position vectors in the cell (as these will give the longest reciprocal
vectors).