Even more Heptominoes!

As per the title really. The set is just sat there in a little box on my desk, tempting me, so when an evening comes along and I've got nothing else to do, it just kind of... happens.

Adding 8 more holes to the heptomino set (plus one hole for the harbour heptomino) gives 765 unit squares, which can form (among other things) a 17x45 rectangle. Here's one with the holes arranged in a grid, like a little keypad for someone who doesn't mind not being able to type zeroes:

Fig. 2: 17x45 with 9 holes.

The question now is how big a grille like this can you put in the middle of a heptomino rectangle before everything gets all out of hand? Actually, that can be a nice challenge for the reader, can't it?


Taking the full set of heptominoes then removing the one with the hole leaves 107 pieces, which (since both 7 and 107) are prime can only make a 7x107 rectangle. Which has been done before, in loads of different ways (there's an example about half way down this page.) Below is a way I found, done as two 7x53's with the I-heptomino separating them.

Fig. 1: The heptominoes (excluding the holey one) in a 7x107 rectangle, with the I-heptomino right in the middle. Click for a full-size image, it's a little bit too long to fit on the page.

I also found this symmetric pinwheel shape, in response to the challenge about half way down Kadon Enterprises' page showing various heptomino solutions.

Fig. 3: A rotationally-symmetric shape with a central hole.

And just for funsies, here's a whopping cross made from all the pentominoes, hexominoes, and heptominoes combined:

Fig. 4: I need to just decide on one scale to draw every image in. And maybe pick a colour scheme and stick to that too, while I'm at it.