Abstract
We introduce some versions of the notion of the combinatorial p-parameter property for polyhedra whose general meaning reduces to search for the number of parameters ensuring unique determination of a polyhedron locally on assuming given edge lengths and combinatorial structure.
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References
Legendre A., Eléments de Géométrie, Paris (1806).
Bricard R., “Mémoire sur la théorie de l'octaèdre articulé,” J. Math. Pures Appl., 5, No. 3, 113–148 (1897).
Sabitov I. Kh., “A generalized Heron-Tartaglia formula and some of its consequences,” Mat. Sb., 189, No. 10, 105–134 (1998).
Maksimov I. G. and Sabitov I. Kh., “On the definition of combinatorially p-parameter polyhedra,” in: Abstracts: The International Conference “Geometry and Applications,” Novosibirsk, 2000, pp. 62–64.
Gluck H., “Almost all simply connected closed surfaces are rigid,” Lecture Notes in Math., 438, 225–240 (1975).
Sabitov I. Kh., “New classes of rigid polyhedra,” in: Abstracts: All-Union Conference on Geometry and Analysis, Novosibirsk, 1989, p. 72.
Sabitov I. Kh., “Algorithmic solution of a problem of isometric realization of two-dimensional polyhedral metrics,” Izv. Ross. Akad. Nauk Ser. Mat., 66, No. 2, 159–172 (2002).
Berger M., Geometry. Vol. 1 [Russian translation], Mir, Moscow (1984).
Blumenthal L. M., Theory and Applications of Distance Geometry, Chelsea, New York (1970).
Sabitov I. Kh., “Algorithms for checking deformability of polyhedra,” in: Proceedings of the Conference in Honour of 25th Anniversary of the Institute of Mathematics with Computer Center of Ufa Scientific Center of the RAS: “Complex Analysis, Differential Equations, Numerical Methods, and Applications. VI: Numerical Methods,” IMVTs UNTs RAN, Ufa, 1996, pp. 156–166.
Sabitov I. Kh., “Algebraic checking of deformability of bipyramids,” Ukrain. Geom. Sb., 30, 109–111 (1987).
Lawrenchenko S., Negami S., and Sabitov I. Kh., “A simpler construction of volume polynomials for a polyhedron,” Beitr. Algebra Geom., 43, No. 1, 261–273 (2002).
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Maksimov, I.G., Sabitov, I.K. On the Notion of the Combinatorial p-Parameter Property for Polyhedra. Siberian Mathematical Journal 43, 661–673 (2002). https://doi.org/10.1023/A:1016324302868
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DOI: https://doi.org/10.1023/A:1016324302868