is replaced by $F_m \oplus
I_{r/2-m}$. In summary, we obtain a matrix ${\tilde M}_r$ that is defined by the equation $$\label{Gleichung}
{\tilde M}_r = Q_r T_r (I_2 \otimes (F_m \oplus I_{r/2-m})) \in {\mathbb
C}^{r \times r}.$$ This matrix is a unitary extension of the matrix $M$ corresponding to the dihedral POVM with some zero operators as discussed in Section \[Sektion ortho\]. Our example with $T_8$ leads to the matrix $$Q_8^\dagger {\tilde M}_8 =  \left( 
\begin{array}{cccc|cccc} \alpha & \alpha & \alpha & 0 & \beta & \beta
& \beta & 0 \\ \alpha & \alpha \omega & \alpha \omega^2 & 0 &
-{\overline \beta} & -{\overline \beta} \omega & -{\overline \beta}
\omega^2 & 0 \\ \alpha & \alpha \omega^2 & \alpha \omega & 0 & \beta &
\beta \omega^2 & \beta \omega & 0 \\ 0 & 0 & 0 & \sqrt{3} \alpha & 0 &
0& 0& -\sqrt{3} \, {\overline \beta} \\ 
\hline &&&& \\ [-0.35cm] {\overline \beta} &
{\overline \beta} & {\overline \beta} & 0 & - \alpha & -\alpha &
-\alpha & 0 \\ \beta & \beta \omega & \beta \omega^2 & 0 & \alpha &
\alpha \omega & \alpha \omega^2 & 0 \\ {\overline \beta} & {\overline
