Note that these additional symmetries do not allow a planar slice to have, say, 8-fold rotation symmetry.
With additional mirror-image symmetry (D) there are n 1 degrees of freedom.
There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed.
With additional symmetry it occurs also in cmm, p3m1, p31m, p4m and p6m.
In order to explain the prevalence of property rights over "anti-property rights" one must discover a way to break this additional symmetry.
This additional symmetry would alter the phenomenology completely.
In the case of additional symmetries a fundamental domain is smaller.
The additional symmetry operators A have implicitly connected the different l multiplets among themselves, for a given energy (and C).
The additional explicit symmetry breaking gives these bosons a small mass.
Supposing a homogeneity of space without any additional symmetry leaves a great freedom in choosing the metric.