The most common case occurs in naive implementations of continuous level of detail, where a finer-level mesh is "sewn" together with a coarser-level mesh by simply aligning the finer vertices on the edges of the coarse polygons.
The most common occurrence happens in uncomplicated implementations of continuous level of detail, where a more refined mesh is "joined" to a less detailed mesh by simply matching the finer vertices on the edges of the coarse polygons.