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.
On Hamiltonian cycles in the FCC grid
Lidija Comic;Paola Magillo
2020-01-01
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.
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