and $c = |c| \cos \varphi \hat{\jmath} + |c| \sin \varphi \hat{k}$, for the basis $\{a,b,c\}$, where $\varphi$ is the angle between $b$ and $c$, as established in the item \[angle\].

[\*[4]{}[|c]{}|]{} & & &\
Class & $\alpha(p)$ & $\delta_{\alpha}(p)$ & $\delta_{\alpha}(p) 
\cos(\alpha,\beta)$\
& & &\
& & &\
${\mathcal{G}_2}$ & $(x+|a|,-y, -z)$ & $\sqrt{|a|^2+4(y^2+z^2)}$ & $-2y$\
& & &\
& & &\
${\mathcal{G}_3}$ & $(x+|a|, -\frac{1}{2} y - \! \frac{\sqrt{3}}{2} z, 
\, \frac{\sqrt{3}}{2} y - \! \frac{1}{2} z)$ & $\sqrt{|a|^2 + 3(y^2+z^2)}$ & $- \frac{\sqrt{3}}{2}(\sqrt{3}y 
+ z)$\
& & &\
& & &\
${\mathcal{G}_4}$ & $(x+|a|,-z,y)$ & $\sqrt{|a|^2+2(y^2+z^2)}$ & $-(y+z)$\
& & &\
& & &\
${\mathcal{G}_5}$ & $(x+|a|, \frac{1}{2} y - \! \frac{\sqrt{3}}{2} z, \, 
\frac{\sqrt{3}}{2} y + \frac{1}{2} z)$ & $\sqrt{|a|^2+(y^2+z^2)}$ & $-\frac{1}{2}(y + \sqrt{3}z)$\
& & &\

Writing $p=(x,y,z)$ for the components of the position of $C_0$ in the basis $\{\hat{\imath},\hat{\jmath},\hat{k}\}$,[^3] one can easily work out the expressions for the components of the position of $C_1$, $\alpha(p)$, the distance function $\delta_{\alpha}(p)$, and the cosine of the angle between $\overline{C_0C_1}$ and $\overline{C_0C_2}$, $\cos(\alpha,\beta)$. The resulting expressions are shown in Table \[Tb:Express\].

For the configuration we are dealing with, one trivially has $d_2=\delta_{\beta}(p)=|b|$, since $\beta$ is a pure 