  We present a systematic study of photonic band gaps (PBGs) in
three-dimensional (3D) photonic amorphous structures (PAS) with short-range
order. From calculations of the density of optical states (DOS) for PAS with
different topologies, we find that tetrahedrally connected dielectric networks
produce the largest isotropic PBGs. Local uniformity and tetrahedral order are
essential to the formation of PBGs in PAS, in addition to short-range geometric
order. This work demonstrates that it is possible to create broad, isotropic
PBGs for vector light fields in 3D PAS without long-range order.
