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- W2965508960 abstract "We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. We establish a bijection between non-Euclidean tetrahedra and certain rational elliptic surfaces. We interpret the edge lengths and the dihedral angles of a tetrahedron as values of period maps for the corresponding surface. As a corollary we show that the cross-ratio of the exponents of the solid angles of a tetrahedron is equal to the cross-ratio of the exponents of the perimeters of its faces. The Regge symmetries of a tetrahedron are related to the action of the Weyl group $W(D_6)$ on the Picard lattice of the corresponding surface." @default.
- W2965508960 created "2019-08-13" @default.
- W2965508960 creator A5012465897 @default.
- W2965508960 date "2019-08-03" @default.
- W2965508960 modified "2023-09-27" @default.
- W2965508960 title "Rational Elliptic Surfaces and the Trigonometry of Tetrahedra" @default.
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