Isotropic systems and homogeneity In isotropic systems, the atomic arrangement is homogeneous in all directions. In the case of glass, which has the atomic structure of a liquid and, therefore, a random atomic structure that is definitely not homogeneous, is it that the atomic arrangements in each direction are equally disordered and therefore homogeneous in that sense?
 A: First, an isotropic system need not be homogenous. We say the electric field from a point charge is isotropic although it is inhomogeneous. However, an isotropic, translation invariant system must be homogeneous. 
While you are correct that a class is truly inhomogeneous as it is described by discrete atomic positions, people say that a glass is homogeneous when it is understood that they are only concerned with properties of a glass which are defined on a length scale much larger than the typical atomic separation. On these length scales, the inhomogeneities wash out (since the atomic positions are assumed to have a very short correlation length). 
An example of such a quantity would be an average density. Suppose you chipped off a centimeter cubed piece of glass and you wanted to know how much it weighed. If the atomic positions are truly uncorrelated, then you would do just fine to take the mass of a full meter cubed of glass and use that to find the density. In fact, this approach would give a pretty good estimate of density down to length scales of tens of nanometers. 
