The classification of compact hyperbolic Coxeter d-polytopes with d + 2 facets.

Frank Esselmann

Displaying similar documents to “The classification of compact hyperbolic Coxeter d-polytopes with d + 2 facets.”

Locally toroidal regular polytopes of rank 4.

Peter McMullen, Egon Schulte (1992)

Commentarii mathematici Helvetici

Similarity:

The semiregualr polytopes.

R. Blind, G. Blind (1991)

Commentarii mathematici Helvetici

Similarity:

Chiral Polytopes from Hyperbolic Honeycombs.

E. Schulte, B. Nostrand (1995)

Discrete & computational geometry

Similarity:

An illustrated theory of hyperbolic virtual polytopes

Marina Knyazeva, Gaiane Panina (2008)

Open Mathematics

Similarity:

The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.

Inner Illumination of Convex Polytopes

Peter Mani (1974)

Commentarii mathematici Helvetici

Similarity:

On hyperbolic virtual polytopes and hyperbolic fans

Gaiane Panina (2006)

Open Mathematics

Similarity:

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,...