Subcomplex with no missing shells

A CW subcomplex has no missing shells if a cell with a shell-length boundary arc contained in the CW subcomplex is itself contained in the CW subcomplex. For $C^{\prime }(1/6)$ it suffices that every excluded cell have a complementary boundary arc of length at least half its perimeter with no edge in the CW subcomplex: an arc lying in the CW subcomplex then has length at most half and cannot be a shell's exterior arc.