Johann F. C. Hessel

[1] 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.

In 1830, Hessel proved that, as a consequence of Haüy’s law of rational indices, 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.

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.

It went unnoticed until it was republished in 1897 as part of a collection of papers on crystallography in Oswalds Klassiker der exakten Wissenschaften (Ostwald's Classics of the Exact Sciences).

Prior to this posthumous re-publication of Hessel's investigations, similar findings had been reported by the French scientist Auguste Bravais (1811–1863) in Extrait J.

The word habit is used to describe the overall external shape of a crystal specimen, which depends on the relative sizes of the faces of the various forms present.

Hessel also found Euler's formula disobeyed with interconnected polyhedra, for example, where an edge or vertex is shared by more than two faces (e.g. as in edge-sharing and vertex-sharing tetrahedra).

His analysis was published in 1826 (Taschenbuch für die gesammte Mineralogie, 20 [1826], 289–333) but, as with his work on the crystal classes, it did not garner much attention among his contemporaries.