  Symmetry equations are obtained for the rigidity matrices associated with
various forms of infinitesimal flexibility for an idealised bond-node crystal
framework $\C$ in $\bR^d$. These equations are used to derive symmetry-adapted
Maxwell-Calladine counting formulae for periodic self-stresses and affinely
periodic infinitesimal mechanisms. The symmetry equations also lead to general
Fowler-Guest formulae connecting the character lists of subrepresentations of
the crystallographic space and point groups which are associated with bonds,
nodes, stresses, flexes and rigid motions. A new derivation is also given for
the Borcea-Streinu rigidity matrix and the correspondence between its nullspace
and the space of affinely periodic infinitesimal flexes.
