English abstract
The projections of the lattices, may be used as models of quasicrystals, and
the particular afne extension of the H2 symmetry as a subgroup of A4, dis cussed in this work, presents a diferent perspective to 5-fold symmetric qua sicrystallography. Afne H2 is obtained as the subgroup of the afne A4. The
infnite discrete group with local dihedral symmetry of order 10 acts on the
Coxeter plane of the root lattice of A4 whose Voronoi cell tessellates the 4D
Euclidean space possessing the afne A4 symmetry. Facets of the Voronoi
cell of the root lattice are identifed. Four adjacent rhombohedral facets of
the Voronoi cell V (0) of A4 project into the decagonal orbit of H2 as thick
and thin rhombuses where long diagonals of the rhombohedra serve as re fection line segments of the refection operators of H2. It is shown that the
thick and thin rhombuses constitute the fnite-fragments of the tiles of the
Coxeter plane with the action of the afne H2 symmetry. Structure of the
local dihedral symmetry H2 fxing a particular point on the Coxeter plane is
determined.
