What should be proper definition of a polyhedron(not necessarily convex)?

Question

I have searched for a rigorous definition of a polyhedron in Euclidean $3$-space and found that (on wikipedia) it is quite difficult to formulate general definition as Euler, Cauchy etc. failed to do so. Now I have a definition in my mind but could anybody please point out where is the flaw?

Definition : A set E will be called a polyhedron in $3$-space if followings hold:

1. It is compact, locally flat (embedded $C^0$) $3$-submanifold with boundary.

2. Its boundary consists of finitely many polygons.

Any help will be appreciated.

P. S. I want a definition that will work for the proof of Dehn-Sydler Theorem.