Editing Carbon nanotube (section)

=== Chirality and mirror symmetry ===

A nanotube is [[chirality|chiral]] if it has type (''n'',''m''), with ''m'' > 0 and ''m'' ≠ ''n''; then its [[enantiomer]] (mirror image) has type (''m'',''n''), which is different from (''n'',''m''). This operation corresponds to mirroring the unrolled strip about the line ''L'' through ''A1'' that makes an angle of 30 degrees clockwise from the direction of the '''''u''''' vector (that is, with the direction of the vector '''''u'''''+'''''v'''''). The only types of nanotubes that are [[achiral]] are the (''k'',0) "zigzag" tubes and the (''k'',''k'') "armchair" tubes. If two enantiomers are to be considered the same structure, then one may consider only types (''n'',''m'') with 0 ≤ ''m'' ≤ ''n'' and ''n'' > 0. Then the angle ''α'' between '''''u''''' and '''''w''''', which may range from 0 to 30 degrees (inclusive both), is called the "chiral angle" of the nanotube.