  We present a systematic, rigorous construction of all 70 strongly rational,
holomorphic vertex operator algebras $V$ of central charge 24 with non-zero
weight-one space $V_1$ as cyclic orbifold constructions associated with the 24
Niemeier lattice vertex operator algebras $V_N$ and certain 226 short
automorphisms in $\operatorname{Aut}(V_N)$.
  We show that up to algebraic conjugacy these automorphisms are exactly the
generalised deep holes, as introduced in arXiv:1910.04947, of the Niemeier
lattice vertex operator algebras with the additional property that their orders
are equal to those of the corresponding outer automorphisms.
  Together with the constructions in arXiv:1708.05990 and arXiv:1910.04947 this
gives three different uniform constructions of these vertex operator algebras,
which are related through 11 algebraic conjugacy classes in
$\operatorname{Co}_0$.
  Finally, by considering the inverse orbifold constructions associated with
the 226 short automorphisms, we give the first systematic proof of the result
that each strongly rational, holomorphic vertex operator algebra $V$ of central
charge 24 with non-zero weight-one space $V_1$ is uniquely determined by the
Lie algebra structure of $V_1$.
