Gadolin demonstrated circa 1860, in a rigorous manner, that axes of symmetry in crystals can only be of order 2, 3, 4 or 6.

Miller introduced the use of the 2 circles optical goniometer for the measurement of angles between crystal faces.

E Mallard developed circa 1870 his theory about "merihedral crystals".

A.M. Schönflies and V.S. Fedorov established circa 1890 the existence of the 230 groups of position symmetry (= space groups).