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We consider the family of area bisectors of a polygon (possi - bly with holes) in the plane We say that two bisectors of a polygon   P   are combinatorially distinct if they induce di er - ent partitionings of the vertices of  P We show that there are simple  polygons  with   n   vertices  that  have   (n2)  combina - torially  distinct  area bisectors (matching the obvious upper bound),  and  we  present  an  output - sensitive  algorithm  for computing an explicit representation of all the bisectors of a given  polygon Our study is motivated by the development of  novel,   exible  feeding  devices  for  parts  positioning  and orienting The  question  of  determining  all  the  bisectors  of polygonal  parts  arises  in  connection  with  the  development of e cient  part positioning  strategies  when using  these de - vices

The area bisectors of a polygon and force equilibria in programmable vector fields