Trigonometry of a tetrahedron Clearly the sum of the angles of any side of the tetrahedron must be 180°. Since there are four such triangles, there are four such constraints on sums of angles, and the number of degrees of freedom is thereby reduced from 12 to 8. The four relations given by the sine law further reduce the number of degrees of freedom, from 8 down to not 4 but 5, since the fourth constraint is not independent of the first three. Thus the space of all shapes of tetrahedra is 5-dimensional. See: Law of sines The law of cosines for the tetrahedron
Facial Angles (Camper) for Philipp von Stosch's "Pierres Antiques Gravées". The facial angles of Moors and Kalmyks was calculated to be 70 degrees, and that of a European 80 degrees. The original report of these lectures in the proceedings of the literature society is listed as one of the 1000 most important texts in the Canon of Dutch Literature. Facial Angles (Camper) Facial Angles refers to the content of two lectures on this subject by the Amsterdam professor of anatomy Petrus Camper on the 1st and 8 August in 1770 to the Amsterdam Drawing Academy called the "Teken-akademie". Camper was a competent artist