Recall that a polytope is defined by the intersection of finitely many closed half spaces.   A planar polytope is the defined by the intersection of finitely many planar closed half spaces.    For more about polytopes, see https://www.researchgate.net/profile/Guenter_Ziegler @Gunter M. Ziegler, especially his Lectures on Polytopes, Springer 2007, DOI 10.1007/978-1-4613-8431-1.

A polytope is a rich source of features that provide a natural transition to feature vectors in R^n, a Euclidean n-dimensional feature space.   Sample features are area, diameter, number of sides, center of mass.   Let G be a planar polytope with a description (area(P), diameter(P), number of sides(P)), a feature vector in R^3.   Let A, B be subsets of a set of planar polytopes X.   And let delta_P be a descriptive proximity on X.   Let \intersection_{P} denote a descriptive intersection so that A \intersection_{P} B is the set of all descriptions common to A and B. Then A \delta_P B implies that A \intersection_{P} B is not empty.   And the pair (X, delta_P) is an example of a descriptive proximity space.   Let RelProx be a set of proximity relations on X.   Then the pair (X, RelProx) is an example a convex proximal relator space.

Then one might ask if there are particular aspects of convex polytopes that lead to convex relator spaces that would be useful in one or more applications.