  In this paper, we introduce a flip operation on self-complementary ideals of
chain product posets and study the resulting flip graphs. We give asymptotics
for the number of vertices in these graphs, compute their diameters, and give
bounds for their radii. We also define similar flip operations on
self-complementary ideals of the chain product $[2r]\times [2r]\times [2r]$
satisfying additional symmetries, and we achieve similar results for the
resulting flip graphs.
