Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Virtual polytope

Sortuj według:

Ogranicz wyniki do:

On hyperbolic virtual polytopes and hyperbolic fans

100%

Panina G.

Open Mathematics

2006

tom 4

nr 2

270-293

Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ3 be a smooth convex body. If for a constant C, at every point of ∂K, we have R 1 ≤ C ≤ R 2 then K is a ball. (R 1 and R 2 stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number of horns is constructed. Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed.

Rigidity and flexibility of virtual polytopes

100%

Panina G.

Open Mathematics

2003

tom 1

nr 2

157-168

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.

Ograniczanie wyników

2 Open Mathematics

2 Panina G.

1 2006

1 2003

Wyniki wyszukiwania

On hyperbolic virtual polytopes and hyperbolic fans

Rigidity and flexibility of virtual polytopes