Geometric configurations that, if unfolded, could not lie flat on a plane without overlapping pieces. Typically this situation occurs if the surface consists of several patches sharing a boundary. Natural examples include a fish with fins, a plane with wings, or a bag with compartments.
The following are examples of nonmanifold topology:
In the first example (the T shape), more than two faces share an edge. In the second example (the bowtie shape), two faces share a single vertex without also sharing an edge. In the third example, a single shape has non-contiguous normals (without border edges). This is a less obvious example of nonmanifold geometry.
