The 17 types of plane symmetry

December 12, 2008

There are 17 types of symmetry which can used to cover a 2 dimensional surface.

Here are some websites that discuss this.

Detailed discussion of computer generated Zelij patterns:
http://www.mi.sanu.ac.yu/vismath/kaplan/index.html

The basic table of symmetries:
http://www2.spsu.edu/math/tile/symm/ident17.htm

From the same website – an example of a pattern from the Al Hambra with p6m symmetry:
http://www2.spsu.edu/math/tile/grammar/moor/moor3f.htm

The Wikipedia page on rotational symmetry
http://en.wikipedia.org/wiki/Symmetry_combinations

82 Zelij pics on Flickr. I must add mine…
http://www.flickr.com/photos/tags/zelij/interesting/

Dutch artist MC Escher was a master of tiling symmetries
Douglas Hofstadter, ‘Visions of Symmetry’

Tile Generator (design your own replicating tile structure):
http://escher.epfl.ch/escher/

Dr Heinrich Heesch identified 28 types of repeating structure
http://www.eschertile.com/tile28.htm

Advertisements

Zelij Extrapolated

December 12, 2008

On the train journey from Marrakesh to Fez, I played around with one particular pattern, adding a layer at each iteration

img002

img011

img014

img013

Drawings made of Zelij tilework

December 12, 2008

 A simple  interlocking open cross.

img003

A slightly more complicated version. Features the 8 point star in the centre, though somewhat distorted.

img007

Repeating 8 point star design.

img009

A very typical zelij pattern

img004

Zelij photographs

December 12, 2008

100_0866

100_0867

100_0971

100_0926

Wild Claims

December 12, 2008

If you search for ‘zelij tiles’ on the internet, you will keep coming across the same poorly translated sales pitch from Saint Tropez Stone:  Saint Tropez Stone Ad Feature

I have no idea if they are a reputable company with a quality product or not, and have no interest in them either, but was intrigued by their claim:

Environmental & Health benefits

* Slip resistance for improved safety on interior and exterior surfaces.
* It is made from a 100% plentiful and natural raw material that, when removed from a site, is not harmful to the landfills.
* It reduces allergies and improves indoor air quality

If anyone can explain to me how chemically inert ceramic tiling can ‘improve air quality’, then I would be most interested. Otherwise, I shall just assume they are making things up to increase sales to gullible people.

I also like the way they stuff the home page of their website with as many related keywords they can think of, like we all used to do in 1999 before Google penalised you for such things.