\right) \quad\mbox{and} & 
D = \left( \begin{array}{ccc}
              1 & 0 & 0 \\
              0 & 0 & -1 \\
              0 & 1 & 1
    \end{array} \right) \; , \nonumber\end{aligned}$$ in the basis formed by the set $\{a,b,c\}$ of linearly independent vectors that appear in Table 1. We will fit the set of multiple images $\{C_0,C_1,C_2\}$ within manifolds of classes ${\mathcal{G}_2}-{\mathcal{G}_6}$, since the class ${\mathcal{G}_1}$ (the 3–torus) is trivial.

[|c|\*[6]{}[|c]{}|]{} Class & ${\mathcal{G}_1}$ & ${\mathcal{G}_2}$ & ${\mathcal{G}_3}$ & ${\mathcal{G}_4}$ & ${\mathcal{G}_5}$ & ${\mathcal{G}_6}$\
& & & & & & ($A_1$,$a$)\
Generators & $a$, $b$, $c$ & ($A_1$,$a$), $b$, $c$ & ($B$,$a$), $b$, $c$ & ($C$,$a$), $b$, $c$ & ($D$,$a$), $b$, $c$ & ($A_2$,$b+c$)\
& & & & & & ($A_2$,$b-c$)\

Let us first deal with the classes ${\mathcal{G}_2}-{\mathcal{G}_5}$. The generators for the corresponding covering groups are $\alpha 
= (A,a)$, $\beta=(I,b)$ and $\gamma=(I,c)$, with $A=A_1,B,C$ and $D$ for the classes ${\mathcal{G}_2}$, ${\mathcal{G}_3}$, ${\mathcal{G}_4}$ and ${\mathcal{G}_5}$ respectively, and $I$ is the identity transformation. For these classes we will consider the following non-trivial configuration: denoting the position of $C_0$ by $p$, $C_1$ is located at $\alpha(p)$ and $C_2$ at $\beta(p)$. The configuration in which $C_2$ is located at $\gamma(p)$ is equivalent to the former, 