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On deformations of spherical isometric foldings

Ana M. Breda, Altino F. Santos (2010)

Czechoslovak Mathematical Journal

The behavior of special classes of isometric foldings of the Riemannian sphere S 2 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 f s defined by f s ( x , y , z ) = ( x , y , | z | ) .

On rainbowness of semiregular polyhedra

Stanislav Jendroľ, Štefan Schrötter (2008)

Czechoslovak Mathematical Journal

We introduce the rainbowness of a polyhedron as the minimum number k such that any colouring of vertices of the polyhedron using at least k colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.

On the convex hull of projective planes

Jean-François Maurras, Roumen Nedev (2008)

RAIRO - Operations Research

We study the finite projective planes with linear programming models. We give a complete description of the convex hull of the finite projective planes of order 2. We give some integer linear programming models whose solution are, either a finite projective (or affine) plane of order n, or a (n+2)-arc.

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