  In this article, we study orbifold constructions associated with the Leech
lattice vertex operator algebra. As an application, we prove that the structure
of a strongly regular holomorphic vertex operator algebra of central charge
$24$ is uniquely determined by its weight one Lie algebra if the Lie algebra
has the type $A_{3,4}^3A_{1,2}$, $A_{4,5}^2$, $D_{4,12}A_{2,6}$, $A_{6,7}$,
$A_{7,4}A_{1,1}^3$, $D_{5,8}A_{1,2}$ or $D_{6,5}A_{1,1}^2$ by using the reverse
orbifold construction. Our result also provides alternative constructions of
these vertex operator algebras (except for the case $A_{6,7}$) from the Leech
lattice vertex operator algebra.
