Genus: Vertigo
Members of the Genus Vertigo have shells that typically range between 1.5 and 3 mm in vertical height. The shells are ovoid to cylindrical in shape and contain a rounded aperture with zero to nine lamellae at maturity (Horsak and Porkyszko 2010). Vertigo arthuri normally have a conically shaped shell containing 4.75 whorls. Their shells are also relatively small, about 1.68 mm (Pilsbry 1948). This would place Vertigo arthuri in Genus Vertigo.
An example of a member of Genus Vertigo, Vertigo moulissiana, provided by Wikipedia.org