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A total dominating function (TDF) of a graph \( G = (V, E) \) is a function \( f : V \to [0,1] \) such that for all \( v \in V \), the sum of the function values over the open neighborhood of \( v \) is at least one. A minimal total dominating function (MTDF) \( f \) is a TDF such that \( f \) is not a TDF if the value of \( f(v) \) is decreased for any \( v \in V \). A convex combination of two MTDFs \( f \) and \( g \) of a graph \( G \) is given by \( h_\lambda = \lambda f + (1-\lambda)g \), where \( 0 < \lambda < 1 \). A basic minimal total dominating function (BMTDF) is an MTDF which cannot be expressed as a convex combination of two or more different MTDFs. In this paper, we study the structure of the set of all minimal total dominating functions (\(\mathfrak{F}_T\)) of some classes of graphs and characterize the graphs having \(\mathfrak{F}_T\) isomorphic to one simplex.