In computational geometry, the star unfolding of a convex polyhedron is a net obtained by cutting the polyhedron along geodesics (shortest paths) through its faces.
It has also been called the inward layout of the polyhedron, or the Alexandrov unfolding after Aleksandr Danilovich Aleksandrov, who first considered it.
, in general position, meaning that there is a unique shortest geodesic from
along these geodesics, and unfolding the resulting cut surface onto a plane.
The resulting shape forms a simple polygon in the plane.
[2][3] The star unfolding may be used as the basis for polynomial time algorithms for various other problems involving geodesics on convex polyhedra.
Instead, the star unfolding cuts the polyhedron along the geodesics, and forms a polygon with multiple copies of
[1] Generalizations of the star unfolding using a geodesic or quasigeodesic in place of a single base point have also been studied.