Using isotope substitution neutron scattering data, we present a detailed structural analysis of the short and intermediate range structures of the five known forms of amorphous ice. Two of the lower density forms--amorphous solid water and hyperquenched glassy water--have a structure very similar to each other and to low density amorphous ice, a structure which closely resembles a disordered, tetrahedrally coordinated, fully hydrogen bonded network. High density and very high density amorphous ices retain this tetrahedral organization at short range, but show significant differences beyond about 3.1 A from a typical water oxygen. The first diffraction peak in all structures is seen to be solely a function of the intermolecular organization. The short range connectivity in the two higher density forms is more homogeneous, while the hydrogen site disorder in these forms is greater. The low Q behavior of the structure factors indicates no significant density or concentration fluctuations over the length scale probed. We conclude that these three latter forms of ice are structurally distinct. Finally, the x-ray structure factors for all five amorphous systems are calculated for comparison with other studies.