  We systematically construct flatbands (FB) for tight-binding models on simple
Bravais lattices in space dimension $d \geq 2$ in the presence of a static
uniform DC field. Commensurate DC field directions yield irreducible
Wannier-Stark (WS) bands in perpendicular dimension $d - 1$ with
$d$-dimensional eigenfunctions. The irreducible bands turn into dispersionless
flatbands in the absence of nearest neighbor hoppings between lattice sites in
any direction perpendicular to the DC field. The number of commensurate
directions which yield flatbands is of measure one. We arrive at a complete
halt of transport, with the DC field prohibiting transport along the field
direction, and the flatbands prohibiting transport in all perpendicular
directions as well. The anisotropic flatband eigenstates are localizing at
least factorially (faster than exponential).
