The Bravais lattices were studied by Moritz Ludwig Frankenheim (1801–1869), in 1842, who found that there were 15 Bravais lattices.
By 1826, he was already using the integer reciprocals of Weiss' coefficients (the intersection of a plane with the three crystallographic axes) to describe the spatial positions of crystal surfaces, from which the British crystallographer William Hallowes Miller (1801-1880) developed the concept of Miller indices in 1839.
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