We discuss symmetry properties of various phases that can result when biaxi
al objects with at least one polar axis are orientationally ordered and pac
ked on layers. The possibility of spontaneous splay, bend and twist is also
investigated for biaxial nematic, smectic banana and dolphin phases. We fu
rther discuss appropriate order parameters and expressions for Ginzburg-Lan
dau free energies for some phase transitions involving these phases.