The Onsager theory of nematic liquid crystals is extended to rigid polyelec
trolytes cross-linked by polyvalent ions. Recent synchrotron x-ray diffract
ion experiments showed that dilute. birefringent networks are formed under
these conditions. The application of Onsager theory to this system leads to
the prediction of the existence of a range of exotic mesophases such as th
e "cubatic,'' the ''tetratic,'' and the ''trigatic." The exotic network pha
ses appear on the border of regions of phase coexistence of network phase w
ith isotropic material (at low polyvalent ion concentration) and with dense
bundles (at high polyvalent ion concentration).