  We show that every orthogonal polyhedron of genus at most 2 can be unfolded
without overlap while using only a linear number of orthogonal cuts (parallel
to the polyhedron edges). This is the first result on unfolding general
orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the
existence of at most 2 special leaves in what we call the "unfolding tree"
(which ties back to the genus), so unfolding polyhedra of genus 3 and beyond
requires new techniques.
