Fig. 1.

The cube ${\mathcal{C}}_w$ for w = 3. The vertices V_i have their ith coordinate equal to $n(\sigma -1)$, where $n=k/w$ and all other coordinates equal to 0. The wedge W_i is the part of the cube of the points whose ith coordinate is greater than the others, which includes vertex V_i. The hyperplanes separating wedge W_i and W_j is orthogonal to the vector ${\displaystyle \overrightarrow{V_i{V}_j}}$. An edge in the de Bruijn graph corresponds to a rotation of $2\pi /w$ around the line $O{O}_{{\mathcal{C}}_w}$, followed by a translation along the $(w-1)$th coordinate of at most σ