Fig. 1. Dimer model $\Gamma_{4a}$.

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Fig. 1. Dimer model $\Gamma_{4a}$. From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fig. 2. A part of perfect matchings of $\Gamma_{4a}$. From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fig. 3. Differences of perfect matchings and the perfect matching polygon of $\Gamma_{4a}$. From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fig. 4. Quiver associated with $\Gamma_{4a}.$ From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fig. 5. An example of paths $p_a^{\pm}$. From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fig. 6. The classification of reflexive polygons. From: Mutations of Splitting Maximal Modifying Modules: The Case of Reflexive Polygons Int Math Res Notices. Published online June 25, 2017. doi:10.1093/imrn/rnx114 Int Math Res Notices | © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.