  We study intersection of two polyhedral spheres without self-intersections in
3-space. We find necessary and sufficient conditions on sequences x =
x_1,x_2,...,x_n, y = y_1,y_2,...,y_n of positive integers, for existence of
2-dimensional polyhedra f,g in R^3 homeomorphic to the sphere and such that
  * f-g has n connected components, of which the i-th one has x_i neighbors in
f and
  * g-f has n connected components, of which the i-th one has y_i neighbors in
g.
  Analogously we study intersection of three polyhedral spheres without
self-intersections in 3-space. Russian version is accessible to high-school
teachers and students interested in mathematics.
