Algorithmic solution of the problem of isometric realization for two-dimensional polyhedral metrics. (English. Russian original) Zbl 1076.51513

Izv. Math. 66, No. 2, 377-391 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 2, 159-172 (2002).
In this paper for polyhedra in general position and with a given combinatorial structure the author proposes an algorithm for finding all their metric characteristics, namely, their volumes, dihedral angles and diagonals, from the lengths of their edges. In this way he develops a new line of geometric investigation, which, in analogy with the well-known term “solution of a triangle”, can be called “solution of a polyhedron”.


51M25 Length, area and volume in real or complex geometry
57R42 Immersions in differential topology
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68W30 Symbolic computation and algebraic computation
52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
52B11 \(n\)-dimensional polytopes
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