The adapter assembly extends outward from an inner structure such as an outer barrel or nipple base to attach the inner structure to a housing such as a bowl. Each sized inner structure fits a specified bowl for attachment of the inner structure to the bowl. The adapter assembly extends outward from the inner structure to fit one of the available sizes needed for attachment to the bowl. The adapter assembly is characterized by a first attachment body and a second attachment body. The adapter assembly attaches to the exterior of the inner structure to increase the surface exterior of the outer surface for attachment of the inner structure to the bowl.