Dan Ismailecu and Adam Vojdany, Class preserving dissections
of convex quadrilaterals,
Forum Geometricorum, 9 (2009) 195--211.
Abstract: Given a convex quadrilateral Q having a certain property P,
we are interested in finding a dissection of Q into a finite number of smaller
convex quadrilaterals, each of which has property P as well. In particular,
we prove that every cyclic, orthodiagonal, or circumscribed quadrilateral
can be dissected into cyclic, orthodiagonal, or circumscribed quadrilaterals,
respectively. The problem becomes much more interesting if we restrict our
study to a particular type of partition we call grid dissection.