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The Tucker-Brocard cubic is the triangle cubic with trilinear equation a b c sum_cyclic a α(b^2 β^2 + c^2 γ^2) = αβγ sum_cyclic a^2(b^4 + c^4). It passes through Kimberling centers X_n for n = 6, 76, 880, and 882.
Pierre René Jean Baptiste Henri Brocard