一种简单的平面正方形环面的三维等距嵌入
A Simple 3D Isometric Embedding of the Flat Square Torus
摘要：
从Gott（2019）的包络多面体（围绕一个点的正方形-4）开始：一个缺少顶面和底面的单位立方体。在垂直方向上拉伸2倍，使其边成为（2x 1单位）矩形。它有8个面（4个外部面，4个内部面）、8个顶点和16条边。F-E+V = 0，意味着（环形）亏格= 1。它与一个平坦的正方形环面等距。像任何多面体一样，它的面和边的固有高斯曲率为零。由于4个直角矩形在每个顶点处相交，因此在那里也没有角度亏损和零高斯曲率。所有经线和纬线周长相等（4个单位长）。
英文摘要：
Start with Gott (2019)'s envelope polyhedron (Squares-4 around a point): a unit cube missing its top and bottom faces. Stretch by a factor of 2 in the vertical direction so its sides become (2x1 unit) rectangles. This has 8 faces (4 exterior, 4 interior), 8 vertices, and 16 edges. F-E+V = 0, implying a (toroidal) genus = 1. It is isometric to a flat square torus. Like any polyhedron it has zero intrinsic Gaussian curvature on its faces and edges. Since 4 right angled rectangles meet at each vertex, there is no angle deficit and zero Gaussian curvature there as well. All meridian and latitudinal circumferences are equal (4 units long).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
