Are all polytopes also convex hulls?

It seems, at least in the 2-D case, that all polytopes are going to be convex. Does this hold if the dimensions are increased?

-
Do you mean regular polygons? –  M.B. Oct 31 '12 at 14:53
I'm specifically referring to polytopes created from a combination of half spaces. –  Wesley Tansey Oct 31 '12 at 14:57

Regular polygons are convex whereas regular polytopes may not be. Furthermore, the Platonic solids are indeed convex. Maybe you want to read about convex polytopes?

edit: seeing your comment I guess you are really interested in interesections of halfspaces?

-
That was it! Thanks! –  Wesley Tansey Oct 31 '12 at 15:01