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math.MG2013★ 21 cited
Flexible cross-polytopes in spaces of constant curvature
Alexander A. Gaifullin
We construct self-intersected flexible cross-polytopes in the spaces of constant curvature, that is, the Euclidean spaces, the spheres, and the Lobachevsky spaces of all dimensions…
math.MG2013
Volume of a simplex as a multivalued algebraic function of the areas of its two-faces
Alexander A. Gaifullin
For n greater than or equal to 4, the square of the volume of an n-simplex satisfies a polynomial relation with coefficients depending on the squares of the areas of 2-faces of thi…
math.MG2013★ 1 cited
Deformations of period lattices of flexible polyhedral surfaces
Alexander A. Gaifullin, Sergey A. Gaifullin
In the end of the 19th century Bricard discovered a phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of…