  We calculate the photonic band gap of triply periodic bicontinuous cubic
structures and of tubular structures constructed from the skeletal graphs of
triply periodic minimal surfaces. The effect of the symmetry and topology of
the periodic dielectric structures on the existence and the characteristics of
the gaps is discussed. We find that the C(I2-Y**) structure with Ia3d symmetry,
a symmetry which is often seen in experimentally realized bicontinuous
structures, has a photonic band gap with interesting characteristics. For a
dielectric contrast of 11.9 the largest gap is approximately 20% for a volume
fraction of the high dielectric material of 25%. The midgap frequency is a
factor of 1.5 higher than the one for the (tubular) D and G structures.
