A diversity \delta δ in M M is a function defined over every finite set of points of M M mapped onto [0,\infty) [ 0 , ∞ ) , with the properties that \delta(X)=0 δ ( X ) = 0 if and only if |X|\leq 1 ∣ X ∣ ≤ 1 and \delta(X\cup Y)\leq\delta(X\cup Z)+\delta(Z\cup Y) δ ( X ∪ Y ) ≤ δ ( X ∪ Z ) + δ ( Z ∪ Y ) , for every finite sets X,Y,Z\subset M X , Y , Z ⊂ M with |Z|\geq 1 ∣ Z ∣ ≥ 1 . Its importance relies in the fact that, amongst others, they generalize the notion of metric distance. We characterize when a diversity \delta δ defined over M M , |M|=3 ∣ M ∣ = 3 , is Banach-embeddable, i.e. when there exist points p_i p i , i=1,2,3 i = 1 , 2 , 3 , and a symmetric, convex, and compact set C C such that \delta(\{x_{i_1},\dots,x_{i_m}\})=R(\{p_{i_1},\dots,p_{i_m}\},C) δ ( { x i 1 , … , x i m } ) = R ( { p i 1 , … , p i m } , C ) , where R(X,C) R ( X , C ) denotes the circumradius of X X with respect to C C . Moreover, we also characterize when a diversity \delta δ is a Banach diversity, i.e. when \delta(X)=R(X,C) δ ( X ) = R ( X , C ) , for every finite set X\subset\mathbb R^n X ⊂ R n , where C C is an n n -dimensional, symmetric, convex, and compact set.