Sağlam, İsmail2025-01-062025-01-0620211307-562410.36890/IEJG.7845982-s2.0-85117960126https://doi.org/10.36890/IEJG.784598https://search.trdizin.gov.tr/tr/yayin/detay/504069https://hdl.handle.net/20.500.14669/1604We investigate the behavior of a complete flat metric on a surface near a puncture. We call a puncture on a flat surface regular if it has a neighborhood which is isometric to that of a point at infinity of a cone. We prove that there are punctures which are not regular if and only if the curvature at the puncture is 4?. We classify irregular punctures of a flat surface up to modification equivalence, where two punctures are called modification-equivalent if they have isometric neighborhoods. We show that there are uncountably many modification-equivalence classes of punctures on flat surfaces. © 2021eninfo:eu-repo/semantics/openAccessconical singularitiesFlat surfaceirregular punctureregular punctureArticle2762Q426650406914