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While fully-unstructured quadrilateral mesh generation algorithms exist (see my video on the paving algorithm) the FEA analyst often partitions the input CAD geometry into simpler shapes (also called "decomposition" or, in Cubit, "webcutting") that the meshing tool can recognize as meshable with "more structured" algorithms. In this case the surface was partitioned into 12 sub-surfaces with shared boundaries. The resulting four thin surfaces at far left and right can be recognized as meshable with a fully-structured ("mapped") algorithm. The remaining eight surfaces are recognized as meshable with Cubit's "polyhedron" meshing algorithm. Notice that the polyhedron scheme essentially joins regions of mapped meshes together at an extraordinary point. In this case, notice how each of these eight interior surfaces are meshed with five mapped meshes joined at a valence-5 extraordinary point. This results in a mesh that, while unstructured, actually contains a lot of structure. [1] The polyhedron scheme is a meshing primitive for 2D (and 3D) n-sided regions -- it allows an arbitrary number of sides. Surfaces must have only one loop, and each vertex must be connected to exactly two curves on the surface. There are some interval assignment requirements as well, which are automatically handled by Cubit.