  A new class of full fans in an euclidean space - tight fans - is introduced.
Such fans are defined using a property of local symmetry in a face of a tiling.
Tight fans are related to the theory of parallelotopes in an euclidean space. A
theorem is proved that a fan of cells meeting in a given face of a tiling by
parallelotopes is a tight fan. A new proof was given for a theorem by Delone on
5 combinatorial types of parallelotopes meeting in a common face of codimension
3.
  Canonical scalings of an euclidean space tiling are special functions defined
on hyperfaces of the tiling. Existance of such functions for a given tiling is
known to be related to existance of a generatix of a tiling. Generatix is a
polyhedral surface with an orthogonal projection coinciding with a given
tiling. A theroem is proved that a fan has a canonical scaling iff it is
polytopical.
