  A symmetry-extended Maxwell treatment of the net mobility of periodic
bar-and-joint frameworks is used to derive a sufficient condition for auxetic
behaviour of a 2D material. The type of auxetic behaviour that can be detected
by symmetry has Poisson's ratio -1, with equal expansion/contraction in all
directions, and is here termed equiauxetic. A framework may have a
symmetry-detectable equiauxetic mechanism if it belongs to a plane group that
includes rotational axes of order n = 6, 4, or 3. If the reducible
representation for the net mobility contains mechanisms that preserve full
rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6,
mechanisms that halve rotational symmetry (B modes) are also equiauxetic.
