CW-complex, Hausdorff space, second-countable space, sober space
connected space, locally connected space, contractible space, locally contractible space
The notion of polytope is the generalization of the notion of polygon to arbitrary dimensions.
a convex 0-polytope is the point
a convex 1-polytope is the interval
a convex 2-polytope is a polygon.
a convex 3-polytope is a polyhedron