Maximal Facet-to-Facet Snakes of Unit Cubes

Let C = 〈C1, C2, . . . , Cn〉 be a finite sequence of unit cubes in the ddimensional space. The sequence C is called a facet-to-facet snake if Ci ∩Ci+1 is a common facet of Ci and Ci+1, 1 ≤ i ≤ n−1, and dim(Ci∩Cj) ≤ max{−1, d+i−j}, 1 ≤ i < j ≤ n. A facet-to-facet snake of unit cubes is called maximal if it is not a proper subset of another facet-to-facet… CONTINUE READING