#polyominoes

[guorble]

i dont think its possible to make a filled rectangle out of tetrominoes with an odd amount of t pieces. i dont have any mathematical proof for this but it just doesnt seem possible. someone smarter than me please find this post i need help

[a-number-a-day]

I might have been a bit bored during math class. (Yes, those are all the free 1-6 -ominoes)

[violetfractal]

[isomorphismes]

[a-number-a-day]

That's right, it's all 108 free heptominoes, drawn using only a pen and my mind.

[a-number-a-day]

Today's number is:

369

(this number was requested by @zazazazazazazazazazazazazazazaaa)

There are 369 free octominoes (figures made of 8 connecting squares). Octominoes are the first set of polyominoes that contains at least one polyomino for every posible type of symetry a polyomino can have (of which there are 8).

[a-number-a-day]

More polyomino tilings!!!

This was actually a failed attempt at aperiodically tiling my favorite polyomino (<3 i love you r pentomino <3) but i think it looks cool so I'm posting it anyway.

Here are two more tilings, more about them an about how i tile is under the cut.

These two tilings use a repeating unit made up of a pentomino and a heptomino (or one duodeconomino if you're crazy), but the repeating unit for a tiling can be any combination of on or more polyominoes. When i want to make a tiling I just take the polyominoes I want to use and put them together in different ways until I have a repeating unit that satisfies one of the tiling criteria.

The two different tilings use the same repeating unit as a way to demonstrate the 2 different methods I use to make tilings. The first one uses the conway criterion which i am not going to explain here, look it up on wikipedia. I don't know if the second one has a formal name so I have dubbed it the parallellogram criterion. It uses only translation, no rotation, I think you can figure out how it works by looking at the diagram.

Also @omniscientraisinn

[a-number-a-day]

4 polyomino tiling for you guys too look at, all of these tile the plane except for the last one, which does tile the plane if you ignore the hole in the round heptomino.

@omniscientraisinn hope you don't die from looking at these