AI 中文总结
本文给出了亏格3的八面九边形多面体曲面的整数坐标实现，具有24顶点36边，每对面共享边，验证了平面性、封闭可定向性及$C_4$对称性。
AI 中文摘要
我们给出了一个亏格为3的多面体曲面的整数坐标实现，该曲面具有八个平面简单九边形面。它有24个顶点和36条边，每个顶点与三个面相邻。每一对面共享一条边：20对面共享一条边，8对面共享两条边。给出了顶点坐标、面行走和平面方程。精确验证确认所有面都是平面的，曲面是封闭且可定向的，没有发生意外相交，并且该实现具有$C_4$对称性。该构造基于早期构造并保持其关联结构。
英文摘要
We present an integer-coordinate realization of a genus-3 polyhedral surface with eight planar simple nonagonal faces. It has 24 vertices and 36 edges, and each vertex is incident with three faces. Every pair of faces shares an edge: 20 pairs share one edge and 8 pairs share two. Vertex coordinates, face walks, and plane equations are given. Exact verification confirms that all faces are planar, the surface is closed and orientable, no unintended intersections occur, and the realization has $C_4$ symmetry. The construction is based on an earlier construction and preserves its incidence structure.
Comments5 pages, 2 figures, includes exact integer coordinate tables
