  Self-dual 1-configurations $(n_d)_1$ possess their Menger graph $\mathcal Y$
most $K_4$-separated among connected self-dual configurations $(n_d)$. Such
$\mathcal Y$ is most symmetric if $K_d$-ultrahomogeneous. In this work, such a
$\mathcal Y$ is presented for $(n,d)=(102,4)$ and shown to relate $n$ copies of
the cuboctahedral graph $L(Q_3)$ to the $n$ copies of $K_d$; these are shown to
share each copy of $K_3$ exactly with two copies of $L(Q_3)$.
