  We prove that any finite polyhedral manifold in 3D can be continuously
flattened into 2D while preserving intrinsic distances and avoiding crossings,
answering a 19-year-old open problem, if we extend standard folding models to
allow for countably infinite creases. The most general cases previously known
to be continuously flattenable were convex polyhedra and semi-orthogonal
polyhedra. For non-orientable manifolds, even the existence of an instantaneous
flattening (flat folded state) is a new result. Our solution extends a method
for flattening semi-orthogonal polyhedra: slice the polyhedron along parallel
planes and flatten the polyhedral strips between consecutive planes. We adapt
this approach to arbitrary nonconvex polyhedra by generalizing strip flattening
to nonorthogonal corners and slicing along a countably infinite number of
parallel planes, with slices densely approaching every vertex of the manifold.
We also show that the area of the polyhedron that needs to support moving
creases (which are necessary for closed polyhedra by the Bellows Theorem) can
be made arbitrarily small.
