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Vanishing of the total angular momentum of the electrons occupying all
orbitals of a closed shell in an atom is a textbook fact. Understanding the
symmetry content of the atomic shell as irreducible representation of angular
momentum, enables straightforward transfer of the notion to (translational or
helically) periodic systems. More relevant generalizations naturally appear:
stratum shell is intermediate step to physically sound band representations,
including elementary and basic ones and connected components. We show that
nontrivial determinant representation indicates stable topology of band in
single colorless layer groups and obstructive limit in in single colorless line
groups.
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