  Iso-edge domains are a variant of the iso-Delaunay decomposition introduced
by Voronoi. They were introduced by Baranovskii & Ryshkov in order to solve the
covering problem in dimension $5$.
  In this work we revisit this decomposition and prove the following new
results:
  $\bullet$ We review the existing theory and give a general mass-formula for
the iso-edge domains.
  $\bullet$ We prove that the associated toroidal compactification of the
moduli space of principally polarized abelian varieties is projective.
  $\bullet$ We prove the Conway--Sloane conjecture in dimension $5$.
  $\bullet$ We prove that the quadratic forms for which the conorms are
non-negative are exactly the matroidal ones in dimension $5$.
