remove redundant topology

Hi
How can I remove redundant topology of a shape?
For example, two solids are merged by BRepAlgoAPI_Fuse to result a new solid. (Please see the attached picture) When I check the topology, there are 10 faces, 20 edges, and 12 vertices (left side of the picture). How can I remove the redundant topology so that the result is 6 faces, 12 edges, and 4 vertices (right side of the picture). Of course, this new solid can be from any functions.

Thanks.

Sean