论文标题
四面体和立方体的景观：对多面体上最短路径的探索
Landscapes of the Tetrahedron and Cube: An Exploration of Shortest Paths on Polyhedra
论文作者
论文摘要
我们考虑确定四面体和立方体表面上点之间最短路径的长度的问题。我们的方法与Alexandrov的Star展开的概念相似，但专注于特定的Polyhedra，并使用其对称性来开发基于坐标的公式。我们通过在这些多面体的表面上定义坐标系来做到这一点。随后，我们确定每个多面体网络中的相关区域，并开发公式，这些公式将点输入点的坐标并作为输出作为输出，以讨论的多面体上的两个点之间的距离。
We consider the problem of determining the length of the shortest paths between points on the surfaces of tetrahedra and cubes. Our approach parallels the concept of Alexandrov's star unfolding but focuses on specific polyhedra and uses their symmetries to develop coordinate based formulae. We do so by defining a coordinate system on the surfaces of these polyhedra. Subsequently, we identify relevant regions within each polyhedron's nets and develop formulae which take as inputs the coordinates of the points and produce as an output the distance between the two points on the polyhedron being discussed.
