  We study self-intersected N-periodics in the elliptic billiard, describing
new facts about their geometry (e.g., self-intersected 4-periodics have
vertices concyclic with the foci). We also check if some invariants listed in
"Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020),
arXiv:2004.12497, remain invariant in the self-intersected case. Toward that
end, we derive explicit expressions for many low-N simple and self-intersected
cases. We identify two special cases (one simple, one self-intersected) where a
quantity prescribed to be invariant is actually variable.
