Stokes polyhedra for $X$-shaped polyminos

Yu. Baryshnikov, L. Hickok, N. Orlow, S. Son
2012 Discrete Mathematics & Theoretical Computer Science  
International audience Consider a pair of $\textit{interlacing regular convex polygons}$, each with $2(n + 2)$ vertices, which we will be referring to as $\textit{red}$ and $\textit{black}$ ones. One can place these vertices on the unit circle $|z | = 1$ in the complex plane; the vertices of the red polygon at $\epsilon^{2k}, k = 0, \ldots , 2n − 1$, of the black polygon at $\epsilon^{2k+1}, k = 0, \ldots , 2n − 1$; here $\epsilon = \exp(i \pi /(2n + 2))$. We assign to the vertices of each
more » ... on alternating (within each polygon) signs. Note that all the pairwise intersections of red and black sides are oriented consistently. We declare the corresponding orientation positive.
doi:10.46298/dmtcs.3005 fatcat:fzkrz5ir6nhxvmdiv4viwkzdgi