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So why is element shape so important? Other researchers have investigated the problems that arise within an FEM simulation if the mesh contains elements with very small or very large dihedral angles (the angle formed along an edge by two faces of a tetrahedral element).

It is important that all elements must meet the specified minimum shape requirements. Just one poorly shaped element can cause a simulation to explode. In general we'd like all elements to be close to equilateral in shape.