Cuboidaloid

We have a rectangular parallelepiped of dimensions $A×B×C$, divided into $1×1×1$ small cubes. The small cubes have coordinates from $(0,0,0)$ through $(A−1,B−1,C−1)$. Let $p$, $q$ and $r$ be integers. Consider the following set of $abc$ small cubes: { ( (p+i) mod A, (q+j) mod B, (r+k) mod C ) | i, j and k are integers satisfying 0 ≤ i < a, 0 ≤ j < b , 0 ≤ k < c} A set of small cubes that can b