  A convex geometry is a closure system satisfying the anti-exchange property.
In this work we document all convex geometries on 4- and 5-element 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 the 672 geometries on a 5-element set, we made representations of 623. Of
the 49 remaining geometries on a 5-element 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.
