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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: A fun penta tile...
Date: Wed, 4 Dec 2024 22:34:34 -0800
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On 12/4/2024 10:26 PM, Moebius wrote:
> Am 05.12.2024 um 06:58 schrieb Chris M. Thomasson:
>> Just playing around and I got the pure pentagonal tile down wrt an 
>> infinite "strip". Here is a crude example:
>>
>> https://i.ibb.co/vLy94Jf/image.png
> 
> Outch ... my eyes are hurting! Very nixe... :-)
> 
>> However, I am not sure how to make it go up and down without adding 
>> another tile... (y axis). I can make it go left and right (x-axis). 
>> Well... I can make it go up and down by introducing a rhombus, sorry 
>> for some imprecision, just goofing around here having fun:
>>
>> https://i.ibb.co/NmdY7Qb/image.png
> 
> Ah... Seems familiar, somehow.

It might be another try of mine where the only way I could do it was to 
add a damn rhombus?

https://i.ibb.co/VMMSrCy/image.png

Trying to make it tile up and down _without_ using a rhombus via y axis 
makes me bang my head against a wall. Here is an older work of mine:

https://i.ibb.co/VMMSrCy/image.png


> 
>> Is this anything new? If not where can I learn more about it?
> 
> There's a whole field in math dealing with this and similar stuff!
> 
> https://en.wikipedia.org/wiki/Tessellation
> https://mathworld.wolfram.com/Tessellation.html
> 
> See the sources too.
> 
> More fun:
> https://uni-tuebingen.de/fakultaeten/mathematisch- 
> naturwissenschaftliche-fakultaet/fachbereiche/informatik/lehrstuehle/ 
> algorithms-in-bioinformatics/software/tegula
> 
>