  A $k$-arc in PG($2,q$) is a set of $k$ points no three of which are
collinear. A hyperfocused $k$-arc is a $k$-arc in which the $k \choose 2$
secants meet some external line in exactly $k-1$ points. Hyperfocused $k$-arcs
can be viewed as 1-factorizations of the complete graph $K_k$ that embed in
PG($2,q$). We study the 526,915,620 1-factorizations of $K_{12}$, determine
which are embeddable in PG($2,q$), and classify hyperfocused $12$-arcs.
Specifically we show if a $12$-arc $\mathcal{K}$ is a hyperfocused arc in
PG($2,q$) then $q = 2^{5k}$ and $\mathcal{K}$ is a subset of a hyperconic
including the nucleus.
