Finding equations of the fake projective plane $(C18,p=3,\{2I\})$
Abstract: We find explicit equations of a new pair of fake projective planes, labeled by $(C18,p=3,{2I})$ in the Cartwright-Steger classification. Our method involves starting with known equations of a commensurable fake projective plane $(C18,p=3,\emptyset,d_3 D_3)$ and working through a chain of cyclic covers and quotients to get to the new one.
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