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.