Trigonometry of tetrahedra, rational elliptic surfaces and the results of Joseph Wolstenholme

I will explain how to construct a rational elliptic surface out of every non-Euclidean tetrahedra. This surface "remembers" the trigonometry of the tetrahedron: the length of edges, dihedral angles and the volume can be naturally computed in terms of the surface. The construction is based on relating mixed Hodge structures, associated to the tetrahedron and the corresponding surface.