I am familiar with finite element simulations and numerical schemes like the Gauss Legendre quadrature. I also know that the Gauss integration yields exact values for polynomials up to degree 2n-1 with n being the number of quadrature points. But I don't understand why, for example, second order terahedrons are evaluated in 4 Gauss points and second order hexahedrons in 27 Gauss points (following the Abaqus element definitions). I can't see any connection to the 2n-1 approach here, since the shape functions have to be of degree 2 (or am I wrong?) Maybe someone could explain, how the "right" number of integration points is derived in these elements.

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