3½-ominoes (12 Piece Edition)

This is the set that you get when you enumerate the ways of attaching a diagonally-sliced monomino to a tromino. There are 12 shapes you get this way, in contrast to the 14 you get if you start with tetrominoes and remove a half-square.

---

I haven't really explored much with this set, just because I used to think it somehow less pleasing in a mathemtical sense than the 14-piece set. But by considering the two sets as results of additive and subtractive versions of the same process, I can kind of sort of appreciate them now. A little bit.

They do a 6x7 rectangle:

Maybe they do a 3x14 one too, but I haven't tried it because quite frankly thin rectangles past a certain point scare the hell out of me. Yep, they do a 3x14:

2x21 can't be done. But it's scary how close you can get; one square misplaced. It's nice at least that you can visually understand why it can't be done, it's not just a maddening case of 'probably impossible but can't say for definite'. The two dark red pieces in the diagram are the source of the problem - one of them needs to fit into the square-with-a-slice-taken-out piece, and that leaves the space to the right of the other piece unfillable without, say, two copies of the sliced I-tetromino.

---

[ Home > Sliced Polyforms > Additive 3½-ominoes ]

---

Lewis Patterson. Last updated 15/09/2026.