  We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs
bundles over a compact Riemann surface $\Sigma$ and consider a natural
involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C}
\mathbb{P}^1$ and establishing an identification with a moduli space of null
polygons in Minkowski $3$-space.
