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We studied Tri-Dirichlet boundary value problem of TriLaplace equation. The problem is reformulated as a systems of Laplace-Poisson equation with Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.doi:10.31227/osf.io/adu5x fatcat:pt4tblxgjvca5er7tlmjjnlxze