Gaining the ability to print models like these was one of many reasons I even considered buying a 3D printer. I have been teaching geometry for nearly a decade and in that time I've resorted to crumby 2D sketches and sheets of printer paper to illustrate the relationships between lines and planes. It was time I really showed my students what I was talki about.
Designing a printable model of a plane that intersects two parallel planes does present some difficulties. Clealry, while a geometric plane has no thickness, such a model cannot exist. It took some experimenting to find the right thickness for sturdy lines and planes. Secondly, to avoid copious scaffolding, I've had to design models that exhibit that classic 45° slant. Finally, for clarity (and fun) I made two-color models. These prints will look best if printed on a dual extruder. If you have a dual extruder but have never tried a two-color print, you can find my directions here. The models can also be printed in a single color.
Raft: off (can be on)