Before revision:  In this paper, we prove that Schneiders' pyramid has no hexahedral meshes with fewer than 12 interior vertices and 14 hexahedra, and introduce a valid mesh with 66 hexahedra.
After revision:  In this paper, we prove that Schneiders' pyramid has no hexahedral meshes with fewer than 18 interior vertices and 14 hexahedra, and introduce a valid mesh with 66 hexahedra.