[math-fun] triadic dragon reminiscence

Half a triadic dragon <http://gosper.org/semitriadic.png> self-similarly trisects into knobby canes (blue, orange+green, red+purple). But the whole triadic dragon self-similarly trisects, so two thirds of this half-dragon (blue+orange+green) is itself a triadic dragon. Deleting the blue cane leaves a (not self similar) congruently bisected backwards Z, orange+green, red+purple. But it is also in fact self-similarly trisected! (orange, green+red, purple). The Triadic Dragon joining 0 to 1 has bounding box West: -1/16, East: 17/16 (with index 239(!)/240), and N|S bounds ±9*i*/(16√3) (less certain here). Is there a plane figure that can be dissected into two, as well as three, but not six congruent pieces? —rwg