  We study several models of random geometric subdivisions arising from the
model of Diaconis and Miclo (2011). In particular, we show that the limiting
shape of an indefinite subdivision of a quadrilateral is a.s.\ a parallelogram.
We also show that the geometric subdivisions of a triangle by angle bisectors
converge (only weakly) to a non-atomic distribution, and that the geometric
subdivisions of a triangle by choosing random points on its sides converges to
a "flat" triangle, similarly to the result of Diaconis and Miclo (2011).
