Let's say I have a complex like this: http://img267.imageshack.us/img267/5606/nonplanarpfum9.th.png [Broken] The original nodes are defined on the same plane, but the actual complex exists in 3 dimensions. If I want to find holes in the complex, would computing the 1st homology group work in this non planar case? There are 3 "holes" in this complex. Would computing the 2nd homology group work? However, I do not have any 3D components, just 2D components embedded in 3 space.