In the case of this solid, there isn't a single material attached to the entire element which is why mdlMaterial_getInternalAttachedMaterialElementId and mdlMaterial_getExternalMaterialAttachment didn't work for you. Here the material has been attached to each individual face of the solid. I don't believe there is a published mdlKISolid_ function in V8i that will let you extract the face material attachment information.
HTH
-B
HTH
-B