There are 23 orbits of them under the automorphism group of the Leech lattice .
These orbits correspond to the 23 Niemeier lattices other than the Leech lattice : the set of vertices of deep hole is isometric to the affine Dynkin diagram of the corresponding Niemeier lattice .
There are 23 orbits of them under the automorphism group of the Leech lattice , and these orbits correspond to the 23 Niemeier lattices other than the Leech lattice : the set of vertices of deep hole is isometric to the affine Dynkin diagram of the corresponding Niemeier lattice .