This paper extends prior work by Cameron and Rais to define new multidimensional representations of the reciprocal scatterer space and the general polarization scatterer space, including distance metric definitions for these representations. The relationship between the maximum symmetric scatterer type and the maximum value that can be attained by the asymmetry parameter is derived to determine the shape of the polarization reciprocal scatterer space. Moreover, a metric is derived for this space that reduces to the symmetric scatterer space metric when the asymmetry parameter is zero. These results are extended to the general polarization scatterer space by defining a metric on the polarization scatterer space that reduces to the polarization reciprocal scatterer metric when the reciprocity parameter θ_rec is zero.