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Figure 1
Schematic drawing, shown in the parameter space (x, y), of symmetries of the cyclic extended bases generated by a unit vector. Any point on the disc corresponds to [\overline 3] symmetry (order 6, two free parameters). Points on solid lines lead to tetrahedral symmetry (order 24, one free parameter). Special points without free parameters give other cubic groups: cP, cF, cI (order 48) and the icosahedral group (order 120).

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