**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.*

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