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-> γ b a
Take a primitive real lattice
γ b* a*
(1 1 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
-> γ b a γ b a
If the real structure changes such that ...
γ* b* a* absent
(2 2 0)
(2 1 0)
(2 0 0)
(2 1 0)
(2 2 0)
(1 2 0)
(1 1 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).