Standardizing the visual representation of genetic parts and circuits is essential for unambiguously creating and interpreting genetic designs. To this end, an increasing number of tools are adopting well-defined glyphs from the Synthetic Biology Open Language (SBOL) Visual standard to represent various genetic parts and their relationships. However, the implementation and maintenance of the relationships between biological elements or concepts and their associated glyphs has up to now been left up to tool developers. We address this need with the SBOL Visual 2 Ontology, a machine-accessible resource that provides rules for mapping from genetic parts, molecules, and interactions between them, to agreed SBOL Visual glyphs. This resource, together with a web service, can be used as a library to simplify the development of visualization tools, as a stand-alone resource to computationally search for suitable glyphs, and to help facilitate integration with existing biological ontologies and standards in synthetic biology.