  We classify integral rootless lattices which are sums of pairs of
$EE_8$-lattices (lattices isometric to $\sqrt 2$ times the $E_8$-lattice) and
which define dihedral groups of orders less than or equal to 12. Most of these
may be seen in the Leech lattice. Our classification may help understand
Miyamoto involutions on lattice type vertex operator algebras and give a
context for the dihedral groups which occur in the Glauberman-Norton moonshine
theory.
