For rank 3, there are exactly 61 convex g-fans up to isomorphism, and each is determined by a simple numerical invariant of the algebra.
$\tau$-tilting finiteness of two-point algebras II
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abstract
In this paper, we explain a strategy on $g$-vectors to discover some new minimal $\tau$-tilting infinite two-point algebras. Consequently, the $\tau$-tilting finiteness of various two-point monomial algebras, including all radical cube zero cases, could be determined. Moreover, we find that the derived equivalence class of the Kronecker algebra contains only itself and its opposite algebra.
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Fans and polytopes in tilting theory III: Classification of convex $g$-fans of rank 3
For rank 3, there are exactly 61 convex g-fans up to isomorphism, and each is determined by a simple numerical invariant of the algebra.