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note
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We define the term "internal coordinates" to mean the fractional coordinates of any position within the unit cell, measured from the lattice point forming the unit cell origin. "External coordinates" are defined as the integer numbers giving the relationship of a lattice point to the lattice origin in terms of multiples of the lattice unit vectors. Thus, for the position on the lattice given by the coordinates (12.250, 13.333), the external coordinates are 12, 13, and the internal coordinates are 0.250, 0.333. Note that the internal coordinates are therefore limited to 0 ≤ x < 1, 0 ≤ y < 1.
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