Another wording: "can be repeatedly broken along 'fault lines' to yield individual pieces vs not."

All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

All of the examples fitting right in in BP1097 (re-styled) would fit right here (besides a single solid block, but that isn't shown there).

All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

All of the examples fitting right in in BP1097 (re-styled) would fit right here (besides a single solid block, but that isn't shown there.)

Robert Dawson, A forbidden suborder characterization of binarily composable diagrams in double categories, Theory and Applications of Categories, Vol. 1, No. 7, p. 146-145, 1995.

The whole rectangle can be filled in by successively replacing pairs of adjacent rectangles with one vs. not so.

All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

The whole rectangle can be filled in by successively replacing pairs of adjacent rectangles with one rectangle vs. not so.

All of the examples fitting right here would fit left in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

Aaron David Fairbanks