论文标题
平坦正方形的简单3D等距嵌入
A Simple 3D Isometric Embedding of the Flat Square Torus
论文作者
论文摘要
从Gott（2019）的信封polyhedron（Squares-4附近）开始：一个单位立方体缺少其顶部和底部的脸。在垂直方向上伸展2倍，以使其侧面变为（2x1单位）矩形。这有8个面（4个外部，4个内部），8个顶点和16个边缘。 f-e+v = 0，意味着a（旋转）属= 1。它是平面圆环的等距。像任何多面体一样，它的脸部和边缘上的固有高斯曲率为零。由于每个顶点的4个直角矩形相遇，因此那里也没有角度缺陷和零高斯曲率。所有子午线和纬度周长相等（长4个单位）。
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).
