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Conference material: "Academician O.B. Lupanov XIV International Scientific Seminar "Discrete Mathematics and Its Applications" (20-25 June 2022, Moscow)"
Authors: Lavrenchenko S.A., Lao A.S.
Twelve congruent torus-type polyhedra with same edge hull in three-dimensional space
Abstract:
A set of twelve congruent toroidal polyhedra on 8 vertices with the same edge skeleton in 3-dimensional space, and each of the polyhedra does not have self-intersections. Under the action of the quadruple Klein group (the group rotations of some regular tetrahedron through an angle of 180 degrees around all three of its bimedians together with the identical rotation) on the set of these 12 polyhedra, this set breaks up into six orbits - six pairs of 'mutually complementary' polyhedra, including sense that in each pair of polyhedra do not have a single common face (although they all have the same rib cage).
Keywords:
polyhedra
Publication language: russian,  pages: 4 (p. 240-243)
Russian source text:
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About authors:
  • Lavrenchenko Sergey Alexandrovich,  Russian State University of Tourism and Service
  • Lao Alex Sergeevich