
Wallpaper group - pg
https://en.wikipedia.org/wiki/Wallpaper_group
======
tedsanders
Though the idea of wallpaper symmetry may seem a bit frivolous, in truth the
mathematics of 2D and 3D symmetry groups plays a huge role in materials
science and physics. Every crystalline material is made of atoms in some
pattern, and the symmetry of that pattern has big consequences for what the
material's electrons do. Understanding the symmetry of a crystal will often
aid you in understanding its properties.

This knowledge can also be inverted to design materials rather than merely
understand them. An example of this is the idea to use crystals without
inversion symmetry to make new ferroelectric materials (because
ferroelectricity requires inversion symmetry breaking). A simple way to make a
crystal without inversion symmetry to stack layers of atoms in an ABCABCABC
pattern. Here's a technical description if you are interested and have access:
[http://www.nature.com/nature/journal/v452/n7188/full/nature0...](http://www.nature.com/nature/journal/v452/n7188/full/nature06817.html)

If you'd like to learn more about the study of symmetry in crystallography,
there's a nice MIT OCW set of video lectures here:
[http://ocw.mit.edu/courses/materials-science-and-
engineering...](http://ocw.mit.edu/courses/materials-science-and-
engineering/3-091sc-introduction-to-solid-state-chemistry-
fall-2010/crystalline-materials/15-introduction-to-crystallography/)

I'll close with a good quotation from a famous condensed matter physicist:

"It is only slightly overstating the case to say that physics is the study of
symmetry." \- Nobel Laureate Philip Anderson

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glifchits
I wanted to say that this was probably discovered by a Hacker News devotee who
was sifting through every instance of "pg" on the internet. Then I noticed who
submitted this.

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pcmonk
I just heard a talk on this the other day at an undergraduate mathematics
research conference (SUnMaRC). Apparently, at Al-Andalus there are examples of
all 17 different groups. Islamic art has some of the coolest math.

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reporter
If anyone wants to delve a little deeper into these topics I highly suggest
Patterns in the plane and beyond: symmetry in two and three dimensions. By
B.G. Thomas and M.A. Hann.

The PDF is available for free.

[http://ulita.leeds.ac.uk/docs/Ars_Textrina/Monographs/Patter...](http://ulita.leeds.ac.uk/docs/Ars_Textrina/Monographs/Patterns_in_the_Plane.pdf)

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mrcactu5
this graphic chart was made in 2003 but it's pretty nice illustration of all
17 wallpaper groups

[http://www.math.columbia.edu/~bayer/symmetry/wallpaper/Wallp...](http://www.math.columbia.edu/~bayer/symmetry/wallpaper/WallpaperChart.pdf)

there is also "geometry and the imagination" whose authors include John Conway
(Princeton ) and fields medalist Bill Thurston

[http://www.math.dartmouth.edu/~doyle/docs/gi/gi.pdf](http://www.math.dartmouth.edu/~doyle/docs/gi/gi.pdf)

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nilkn
To anyone interested, my favorite treatment of this appears in Artin's
extraordinary book _Algebra_.

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ballard
Epicdollar startup of the future is:

wallpaper color displays, Philip K. Dick-style.

Top planetary database says this is the closest approximation:
[http://www.eink.com/display_products_triton.html](http://www.eink.com/display_products_triton.html)

No more steaming wallboards and peeling (wo peeling the wallboard backing)
when wifey says she likes this other pattern she just found.

