Od Keplerových mozaik k pětičetné symetrii
Odd cycles and a class of facets of the axial 3-index assignment polytope
On a dynamics in rational polygonal billiards
On a Hadwiger-Wills inequality concerning lattice points.
On Antipodal and Adjoint Pairs of Points for Two Convex Bodies.
On area and side lengths of triangles in normed planes
Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
On braxtopes, a class of generalized simplices.
On Convex Bodies that Permit Packings of High Density.
On Convex Body Chasing.
On deformations of spherical isometric foldings
The behavior of special classes of isometric foldings of the Riemannian sphere under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding defined by .
On face vectors of trivalent maps
On faces of a convex polyhedron in with a small number of sides.
On face-vectors and vertex-vectors of polyhedral maps on orientable -manifolds
On homotopy types of 2-dimensional polyhedra
On hyperbolic virtual polytopes and hyperbolic fans
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...
On Hyperplanes and Polytopes.
On Lattice Points in Polyhedral Cross-Sections.
On lattice polytopes having interior lattice points.
On light subgraphs in plane graphs of minimum degree five
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars and and a light 4-path P₄. The results obtained for and P₄ are best possible.
On longest circuits in certain non-regular planar graphs