# Interlocking puzzle piece with rotational symmetry

I'm designing a jigsaw puzzle where all the pieces have identical shape, but I've found that I also need to be able to rotate some of the pieces. Can anyone suggest a shape with the following properties?

• It can tesselate the plane in a square grid.
• The pieces interlock, like jigsaw puzzle pieces.
• It has 90° rotational symmetry.

Simpler is better, to make cutting easier. Closer to a square is better, because I want to put text in the middle of each piece.

Here's what I was thinking of before I realized that I needed to rotate some pieces:

• I guess there is no straight border on your puzzle?
– JLee
Commented Oct 24, 2022 at 20:00
• My puzzle will have a solid frame around the edge, @JLee. The identical pieces fill in the frame, and the frame gives clues about which piece goes where. Commented Oct 27, 2022 at 4:27
• Ok cool. I got your donimoes book and bought some dominoes, but haven't had time to start into it yet. Hopefully soon.
– JLee
Commented Oct 27, 2022 at 14:25
• Hey great! I hope you enjoy the book, @JLee. Commented Oct 28, 2022 at 6:34

So, you'll want to

• deform each edge in the same way (because of the rotation requirement)
• preserve the point symmetry of each edge wrt the centre of the edge (because of the tiling requirement), and
• have the edge turn more than 90 degrees from the grid (because of the interlocking requirement.)

Borrowing from the most famous point symmetrical interlocking shape, here's a piece that should work:

I wouldn't be surprised if it were to turn out that this is indeed the simplest possible piece shape that filled your requirements, but no guarantees :-)

• Such an elegant solution, I love it! Commented Oct 24, 2022 at 19:01

You can rotate the bump and dent on each side so that the curve that forms the edge of the piece has fewer bends in it. Unfortunately this eats into the central area and makes it smaller.

• That looks about Reich. Commented Oct 24, 2022 at 23:23

Here's the best I could come up with, but I'm hoping that someone will have a simpler idea.

• You have essentially defeated the purpose of asking this question. Commented Oct 24, 2022 at 7:24
• My purpose was to find a more elegant shape to use in a puzzle I'm designing, and it worked. If your purpose was to solve a geometry puzzle, @ParclyTaxel , I see your point. I've added spoiler protection for future readers. Commented Oct 24, 2022 at 19:06
• @ParclyTaxel this is basically the only way to indicate the problem has been resolved in a situation like this where none of the given answers was implemented. Commented Oct 27, 2022 at 1:15

Another variation. A bit like Jaap's, but more squarish and relying on stoppers instead of the shape of the tabs. Or like Don's with wide and flat tabs. Given the symmetry requirements, all solution are somehow similar.