Definition of convex polytope

I know, in general, a convex polytope is an intersection of halfspaces described by a system of "inequalities". But what if these inequalities are replaced by equations, namely, a system of equations, just like solving it using algebra? Geometrically is it also a convex polytope by definition? Moreover, what does it look like? It's definitely not a concrete volumn but a shell, right?

Re: Definition of convex polytope

Hey Rita.

Do you just want to turn a poly-type into something representing a parameterization of the poly-type in the given embedded space?

As an example if you have say a 3D cube example, you pick say a parameterization of (u,v) and then have a parameterization (that will not be smooth but it will be continuous) to describe x(u,v), y(u,v), z(u,v) for u in [0,1] and v in [0,1].