In 1823 he completed a dissertation titled Dissertatio de Theoria Gasorum et Vaporum Meditationes ("Contemplations on the scientific theory of gases and vapors").

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.

On page 15 of his 1842 treatise System Der Krystalle, however, he says – in reference to what he calls the Grundform (basic shape) of crystals – that “there are a total of fifteen, three of which are tesseral (i.e., cubic) crystals, two are tetragonal, two are hexagonal, four are isoclinic (i.e., orthorhombic), three belong to monoclinic and one to triclinic crystals.” All these are the correct numbers except the three for monoclinic, which should be two.

Bravais got the number right (14) in a paper he read to the French Academy of Sciences in 1848 (published in 1850) and also gave a good discussion of why there are exactly 14 lattices.

Bravais mentions in a footnote that Frankenheim in his 1842 treatise listed 3 “modes of the oblique prismatic system of Hauy” (i.e., monoclinic crystals).

Interestingly, in 1856 Frankenheim revisited the question in a journal article (“Über die Anordnung der Moleküle im Krystall,” Ann.