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Using a combinatorial description in terms of slope sequences, we classify all such maps and show that there are exactly ten combinatorial types. This yields a polyhedral model of \\(\\mathcal{M}_3^{\\mathrm{trop}}\\) parametrized by gap lengths between break points.\n  We determine the automorphism groups and obtain a stratification by explicit linear conditions. 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Using a combinatorial description in terms of slope sequences, we classify all such maps and show that there are exactly ten combinatorial types. This yields a polyhedral model of \\(\\mathcal{M}_3^{\\mathrm{trop}}\\) parametrized by gap lengths between break points.\n  We determine the automorphism groups and obtain a stratification by explicit linear conditions. 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