Table A1.

The rotation operators $\mathbf{P}\in {\mathcal{P}}^{24}$ which map a cube onto itself.

${\mathbf{P}}_1=\mathbf{I}$	${\mathbf{P}}_7=\widehat{\mathbf{R}}({90}^o,\left[0\overline{1}0\right])$	${\mathbf{P}}_{13}=\widehat{\mathbf{R}}({180}^o,\left[101\right])$	${\mathbf{P}}_{19}=\widehat{\mathbf{R}}({90}^o,\left[010\right])$
${\mathbf{P}}_2=\widehat{\mathbf{R}}({180}^o,\left[10\overline{1}\right])$	${\mathbf{P}}_8=\widehat{\mathbf{R}}({180}^o,\left[100\right])$	${\mathbf{P}}_{14}=\widehat{\mathbf{R}}({180}^o,\left[010\right])$	${\mathbf{P}}_{20}=\widehat{\mathbf{R}}({180}^o,\left[001\right])$
${\mathbf{P}}_3=\widehat{\mathbf{R}}({120}^o,\left[101\right])$	${\mathbf{P}}_9=\widehat{\mathbf{R}}({180}^o,\left[011\right])$	${\mathbf{P}}_{15}=\widehat{\mathbf{R}}({90}^o,\left[100\right])$	${\mathbf{P}}_{21}=\widehat{\mathbf{R}}({90}^o,\left[\overline{1}00\right])$
${\mathbf{P}}_4=\widehat{\mathbf{R}}({180}^o,\left[01\overline{1}\right])$	${\mathbf{P}}_{10}=\widehat{\mathbf{R}}({120}^o,\left[\overline{1}1\overline{1}\right])$	${\mathbf{P}}_{16}=\widehat{\mathbf{R}}({120}^o,\left[\overline{1}\overline{1}0\right])$	${\mathbf{P}}_{22}=\widehat{\mathbf{R}}({120}^o,\left[1\overline{1}\overline{1}\right])$
${\mathbf{P}}_5=\widehat{\mathbf{R}}(-{120}^o,\left[111\right])$	${\mathbf{P}}_{11}=\widehat{\mathbf{R}}({90}^o,\left[011\right])$	${\mathbf{P}}_{17}=\widehat{\mathbf{R}}({90}^o,\left[00\overline{1}\right])$	${\mathbf{P}}_{23}=\widehat{\mathbf{R}}({180}^o,\left[\overline{1}\overline{1}0\right])$
${\mathbf{P}}_6=\widehat{\mathbf{R}}({180}^o,\left[1\overline{1}0\right])$	${\mathbf{P}}_{12}=\widehat{\mathbf{R}}({120}^o,\left[11\overline{1}\right])$	${\mathbf{P}}_{18}=\widehat{\mathbf{R}}({120}^o,\left[\overline{1}11\right])$	${\mathbf{P}}_{24}=\widehat{\mathbf{R}}({120}^o,\left[1\overline{1}1\right])$