  In this paper, we consider integral maximal lattice-free simplices. Such
simplices have integer vertices and contain integer points in the relative
interior of each of their facets, but no integer point is allowed in the full
interior. In dimension three, we show that any integral maximal lattice-free
simplex is equivalent to one of seven simplices up to unimodular
transformation. For higher dimensions, we demonstrate that the set of integral
maximal lattice-free simplices with vertices lying on the coordinate axes is
finite. This gives rise to a conjecture that the total number of integral
maximal lattice-free simplices is finite for any dimension.
