3 papers
math.MG2025
Steffen's flexible polyhedron is embedded. A proof via symbolic computations
Victor Alexandrov, Evgenii Volokitin
A polyhedron is flexible if it can be continuously deformed preserving the shape and dimensions of every its face. In the late 1970's Klaus Steffen constructed a sphere-homeomorphi…
math.DG2024
Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates
Victor Alexandrov
The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a linear differential equation of the first order, which previous…
math.MG2024
A flexible polyhedron without self-intersections in Euclidean 3-space, all of whose dihedral angles change during a flex
Victor Alexandrov, Evgenii Volokitin
We construct a sphere-homeomorphic flexible self-intersection free polyhedron in Euclidean 3-space such that all its dihedral angles change during some flex of this polyhedron. The…