Johann F. C. Hessel

Johann Friedrich Christian Hessel (27 April 1796 – 3 June 1872) was a German physician (MD, University of Würzburg, 1817) and professor of mineralogy (PhD, University of Heidelberg, 1821) at the University of Marburg.

The origins of geometric crystallography (the field concerned with the structures of crystalline solids), for which Hessel's work was noteworthy, can be traced back to eighteenth and nineteenth century mineralogy. Hessel also made contributions to classical mineralogy (the field concerned with the chemical compositions and physical properties of minerals), as well.

In 1830, Hessel proved that, as a consequence of Haüy’s law of rational intercepts, morphological forms can combine to give exactly 32 kinds of crystal symmetry in Euclidean space, since only two-, three-, four-, and six-fold rotation axes can occur. A crystal form here denotes a set of symmetrically equivalent planes with Miller indices enclosed in braces, {hkl}; form does not mean "shape". For example, a cube-shaped crystal of fluorite (referred to as Flussspath by Hessel) has six equivalent faces. The entire set is denoted as {100}. The indices for each of the individual six faces are enclosed by parentheses and these are designated: (010), (001), (100), (010), (001), and (100). The cube belongs to the isometric or tessular class, as do an octahedron and tetrahedron. The essential symmetry elements of the isometric class is the existence of a set of three 4-fold, four 3-fold, and six 2-fold rotation axes. In the earlier classification schemes by the German mineralogists Christian Samuel Weiss (1780 - 1856) and Friedrich Mohs (1773 - 1839) the isometric class had been designated sphäroedrisch (spheroidal) and tessularisch (tesseral), respectively. As of Hessel's time, not all of the 32 possible symmetries had actually been observed in real crystals.

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