On the so-called Sierpiński gasket fractal \(S \subset\mathbb R^{N-1}\), \(N\geq 3\), a Laplcian can be defined among others by the methods of J. Kigami [“Analysis on fractals” (2001; Zbl 0998.28004)]. Like the Cantor set, every point of \(S\) has at least one “address” in \(\{1, \dots, N\}^{\mathbb N}\), because it is the unique limit point of a decreasing sequence of \(N\)-simplices. Multiple addresses of a single point in \(S\) are identified by the equivalence relation \(\sim\). The authors [Potential Anal. 14, 211-232 (2001; Zbl 0980.60094) and Publ. Res. Inst. Math. Sci. 35, 769-794 (1999; Zbl 0980.60095)] defined a Markov chain \((X_n)_{n\geq 0}\) on the tree \({\mathcal W}\) of finite words over \(\{1,\ldots,N\}\) whose transition probabilities are arranged in such a way that \(\{1,\ldots,N\}^\mathbb N / \sim\), that is, \(S\) turns out to be the Martin boundary of \((X_n)_n\). The authors use the Martin kernel representation to restate the potential theory on \(S\) in terms of the richer potential theory on \({\mathcal W}\). The main tool is an explicit formula of the Martin kernel. In solving the Dirichlet and the Neumann problem on \({\mathcal W}\), the solution to the Poisson problem on \(S\) can be reinterpreted explicitly.