The set of germs of affine or Riemannian homogeneous spaces is naturally the cone over a projective variety. A complex associated to a point in this moduli space calculates the successive filtration quotients of the formal tangent space at that point filtered by order of tangency. I will describe the construction of this moduli space and discuss the homology of this complex for the points of a particularly interesting family of Riemannian homogeneous spaces.