Faces Holes:

If some of the faces of a solid contain holes, the above form of winged-edge data structure does not work. These holes may penetrate the solid (the left box below) or just like a pothole (the right box below).

There are two ways for resolving out this problem:

• For a face along with inner loops, the outer boundary is ordered clockwise, whereas its inner loops, if any, are ordered counter clockwise.
• Another simple method is adding an auxiliary edge among each inner loop and the outer loop as illustrated below. This auxiliary edge shall have the same face for its left and right faces. In this process, a face with holes becomes a single loop that can be represented with the winged-edge data structure. While traversing a loop, auxiliary edges may be identified easily as its left and right faces are the same.