We explore the relationship between a knitted yarn network and its “scaffold surface” to address topological, geometric, and mechanical questions about knit textile behavior. The scaffold structure allows for a mean-field understanding of yarn mechanics, reducing the need to simulate direct yarn-to-yarn contacts by focusing on the geometry of the scaffold surface as an intermediary object. The scaffold structure as part of the Schwarz diamond minimal surface further offers insight into the geometric tendencies of knit and purl stitches, as well as their interfaces.