Convex geometries representable by at most five circles on the plane

A convex geometry is a closure system satisfying the anti-exchange property.In this work we document all convex geometries on 4-and 5element base sets with respect to their representation by circles on the plane.All 34 non-isomorphic geometries on a 4-element set can be represented by circles, and of 672 known geometries on a 5-element set, we made representations of 623.Of the 49 remaining geometries on a 5element set, one was already shown not to be representable due to the Weak Carousel property, as articulated by Adaricheva and Bolat (Discrete Mathematics, 2019).In this paper we show that 7 more of these convex geometries cannot be represented by circles on the plane, due to what we term the Triangle Property.