Abstract The face centered cubic (FCC) grid is a space-filling grid, one of the alternatives to the traditional cubic one. We show that there are five Hamiltonian cycles (non-equivalent up to rotation and symmetry), connecting the faces of a voxel in the FCC grid. Each of the five cycles can be used to trace the boundary of a class of objects in the grid, constructed by iteratively attaching voxels so that each new voxel shares exactly one face with the set of already attached voxels.

中文翻译：

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关于 FCC 网格中的哈密顿循环

摘要 面心立方（FCC）网格是一种空间填充网格，是传统立方网格的替代品之一。我们表明有五个哈密顿循环（不等价于旋转和对称），连接 FCC 网格中体素的面。五个循环中的每一个都可用于跟踪网格中一类对象的边界，通过迭代地附加体素来构建，以便每个新体素与一组已附加的体素共享一个面。