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In a tetrahedron based NLC, the first order gives the Pauling residual entropy of ${1\\over 2}\\log{3\\over 2}\\approx 0.20273$. A 16-th order NLC calculation changes the residual entropy to 0.205507 a correction of 1.37 percent over the Pauling value. At high temperatures, the accuracy of the calculations is verified by a high temperature series expansion. 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