Supplemental on - line material for : High stability of faceted nanotubes and fullerenes of multi - phase layered phosphorus : A computational study

The nomenclature we introduce for faceted nanotubes is not as straight-forward as for non-faceted nanotubes. According to the main manuscript, the circumference of the polygonal cross section of an armchair nanotube is equal to nαaα + nβ1aβ + nγaγ + nβ2aβ . In analogy, the circumference of the polygonal cross section of a zigzag nanotube would be equal to nγ1aγ+nδ1aδ+nγ2aγ+nδ2aδ. Connecting the strips with these widths will result in a unique nanotube and is not ambiguous. Ambiguity arises from assigning atoms along the connection line to either the phase on the one or on the other side of the connection line. As shown in Fig. S1, the same structure could be described by (nα, nβ) and (nα+1, nβ−1). This would lead to different values of nα in the same a-PNT and different values of nγ1 and nγ2 in the same z-PNT. As we suggest in the main manuscript, we can avoid this ambiguity by selecting nα = max in a-PNTs and nγ1 = max and nγ2 = max in z-PNTs.