christianp,
@christianp@mathstodon.xyz avatar

It's really annoying how the neatest way of arranging aperiodic monotiles with gaps between them seems to be to do it periodically

The spectre monotile, arranged in a grid with a bit of space between each tile.The packing looks tighter.

RobertJackson58585858,
@RobertJackson58585858@masto.ai avatar

@christianp

If you show this to an ordinary member of the public, preferably one who has struggled with jigsaw puzzles, I suspect they might suspect, like me, that this approach of putting spaces between the jigsaw pieces is ... ummm ... unconventional?

🤨🤭

christianp,
@christianp@mathstodon.xyz avatar

My thought process this morning:
"I'll just use the tiling I've got and scale down each piece so there's a gap between them."
"Oh, they're concave, so that doesn't work."
"But if I keep scaling down, eventually they won't overlap."
"Look at all that wasted space!"

reluctant p1 symmetry

christianp,
@christianp@mathstodon.xyz avatar

but no, I'm wrong! I don't want to print exactly the right shape, I want to print a shape that will fit together. If I inset the monotile shape and print that, I can use the aperiodic tiling and be sure they'll fit together nicely

christianp,
@christianp@mathstodon.xyz avatar

That looks better!

taatm,
@taatm@mathstodon.xyz avatar

@christianp You need to make this a pasta!

christianp,
@christianp@mathstodon.xyz avatar

@taatm now we're talking! What's Italian for "one tile?"

robinhouston,
@robinhouston@mathstodon.xyz avatar

@taatm @christianp I do not think this is correct

matthras,
@matthras@aus.social avatar

@christianp I came to a similar conclusion when duplicating them for 3D printing purposes 😂

christianp,
@christianp@mathstodon.xyz avatar

@matthras exactly what I'm doing!

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