The Non-Manifold Topology (NMT) Radial Edge data structure, along with the supporting set of Euler operators, provides a versatile environment for modeling non-manifold domains. The operators provide the basic tools to construct and manipulate model topology. However, an implementation of the base functionality in a geometric modeling environment raises some geometry-related issues that need to be addressed to ensure the topological validity of the underlying model. This paper focuses on those issues and emphasizes the use of geometry in the implementation of topological operators. Enhancements to the topology manipulation operations are also discussed. Specifically, this paper describes (i) a geometry-based algorithm for face insertion within the Radial Edge data structure, (ii) a manifestation of the face-insertion algorithm to resolve topological ambiguities that arise in the design of topological glue operators, and (iii) enhancements to the topology deletion operators to meet application-specific requirements.