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Remember in polygonalization of the surface, following rules must be followed. Any two polygons
(i) share a common edge,
(ii) Share a common vertext,
(iii) Arc disjoint.
Figure (a) on the next page, gives an example of an admissible approximation of a surface using triangles, called triangulation. Further, Figure (b) and (c) give examples of some cases that are not admissible as per the rules given above. This means an edge of a polygon cannot be a part of an edge of another polygon.
Similarly, no two polygons can overlap leading to a common non-empty interior.
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