RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 Forthcoming seminars Seminar calendar List of seminars Archive by years Register a seminar Search RSS Forthcoming seminars

You may need the following programs to see the files

Steklov Mathematical Institute Seminar
March 15, 2001, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)

A cycle of work on the theory of regular decompositions of spaces

S. S. Ryshkov, M. I. Shtogrin, N. P. Dolbilin

He also proved that for each type of $n$-dimensional parallelohedron there are a finite number of so-called root (basic) parallelohedra of dimension at most $n$ and arranged in $\mathbf E^n$ in such a way that each parallelohedron of the indicated type is representable up to an affine transformation as a Minkowski sum with non-negative coefficients of these root parallelohedra. From a slight refinement of this result it follows, for example, that up to an affine transformation each fourdimensional parallelohedron can be decomposed into such a sum of a regular 24-hedron and its edges (Ryshkov).
It was shown that a simply connected $d$-dimensional space of constant curvature has a regular decomposition into polyhedra congruent to a given convex polyhedron $P$ if and only if around $P$ one can construct from polyhedra congruent to it a so-called $(d-2)$-corona having a certain radius and satisfying two specific conditions (the condition of stability of the corona group and the condition of local compatibility) (Dolbilin).