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We give a strong fundamental domain for the quotient of$PGL_2\!\left(\mathbb{F}_q(\!(t^{-1})\!)\!\right)$ by$PGL_2\!\left(\mathbb{F}_q[t]\right)$ as a subset of distinct ordered triplepoints of $\mathbb{P}^1(\mathbb{F}_q(\!(t^{-1})\!))$.

A fundamental domain for $PGL(2,\mathbb{F}_q[t])\backslash PGL\!\left(2,\mathbb{F}_q\!\left(\!(t^{-1})\!\right)\!\right)$