  The bottom complex of a finite polyhedal pointed rational cone is the lattice
polytopal complex of the compact faces of the convex hull of nonzero lattice
points in the cone. The algebra, associated to the bottom complex of a cone,
defines a flat deformation of the affine toric variety, associated to the
polyhedral cone, set-theoretically. We describe three explicit infinite
families of abstract polytopal complexes, defining such flat deformations
scheme-theoretically.
