Abstract:
An explicit description of a Dirichlet–Voronoi (DV) cell
of the root lattice $A_n$
in the form of the convex hull
of an
$n$-dimensional parallelotope with a vertex at 0 and
its copies centrally symmetric with respect to 0 is given.
Remarkable properties of this DV-cell are described,
which manifest themselves when layers of the lattice $A_n$
are superposed.
It is shown that the one-parameter family of their metric forms runs through
the cone of positivity from one boundary to the other,
passing through four
$L$-type domains.
Keywords:Dirichlet–Voronoi cell, root lattice $A_n$, superposition of layers.
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