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. Math., Pures et Applique ́es (in 1849) and by the Russian crystallographer Alex V. Gadolin (1828 - 1892) in 1867.
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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).
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He was a student at the Realschule in Nuremberg and subsequently studied science and medicine at Erlangen and Würzburg.
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