On Hamiltonian cycles in the FCC grid

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.