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A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s.
There are several different variations of Penrose tilings with different tile shapes. The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two different rhombi, or two different quadrilaterals called kites and darts. The Penrose tilings are obtained by constraining the ways in which these shapes are allowed to fit together. This may be done in several different ways, including matching rules, substitution tiling or finite subdivision rules, cut and project schemes, and coverings. Even constrained in this manner, each variation yields infinitely many different Penrose tilings.

Penrose tilings are self-similar: they may be converted to equivalent Penrose tilings with different sizes of tiles, using processes called inflation and deflation. The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles. The study of these tilings has been important in the understanding of physical materials that also form quasicrystals. Penrose tilings have also been applied in architecture and decoration, as in the floor tiling shown.

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  1. C

    North West I have recently completed a short tiling course at the DIY school in Stockport.

    I have recently completed a short tiling course at the DIY school in Stockport. I am looking for a tiler in the Lancashire area, preferably Blackburn/Accrington to work with to gain experience in the real world of tiling. Obviously I am not expecting the full going rate for a tiler. Thanks in...
  2. C

    My 1st Job Hi, I have recently completed a short tiling course at the DIY school Stockport. Looking for experience with a professional tiler.

    I have recently completed a short tiling course at the DIY school in Stockport. I am looking for a tiler in the Lancashire area, preferably Blackburn/Accrington to work with to gain experience in the real world of tiling. Obviously I am not expecting the full going rate for a tiler. Thanks in...
  3. nojahoda

    UK Pro Tiling Training

    Hello tilers, I have just joined the forum, but I’ve been having a snoop for the last 6 months or so admiring the work and expert advice wondering if I could try my hand at it some day! Pleased so say I’ll be attending the UK Pro Tiling Training Centre at the start of next month to do the 13...
  4. G

    Training Academy Advice

    Hi. Looking at doing a 9 day intense course at an Academy. I have seen in the pictures on the companies website that they are tiling over existing tiles, presumably from the previous candidates. Is this normal practice? Many thanks. Matt.
  5. T

    Expert UK Tiling Courses (Cardiff) - Tiling Courses Feedback Thread

    Hi guys Long time viewer of the forum, first post. I want to put myself through a tiling course and wondered if anyone has any feedback of Expert Tiling Courses UK in Cardiff? Their website and operation looks very similar to UK Pro Tiling. Are they linked? Thanks.
  6. Dan

    A1 Tiling Courses

    For quite some time we had dozens of websites. We closed a whole bunch (including tilingcoursescompanies.co.uk) some time ago due us (me) being so busy with the main few forums. That said; I bring you www.a1tilingcourses.co.uk - the website that will let you know who to spend your money with...
  7. R

    Training Courses

    Hi all I am new to this so apologies if I have posted in the wrong place! I am currently do a Little DIY tiling, which I enjoy. My day job is in a rather precarious position due to what’s going on In the world, and I am looking at a change of career be it possibly part time initially In...
  8. J

    Retraining

    Hi all I’m looking to retrain after being made redundant from my position in the printing industry. I’ve done my own tiling and enjoy it, as I like a finished product. I’m going straight for the jugular here, is there anyone who would be willing to take on a fifty year old and retrain them. I...
  9. S

    Best training

    Hi there, I am looking for guidance, I am thinking about changing careers, I want to do tiling full time and set up on my own, so I am looking for the best fast track course that's available, any thots
  10. P

    Fast track tiling course advice

    Hi Guys, I'm here to ask for advice on on fast track tiling courses, such as, UK pro tilers, construction skills college and able skills. I'm leaning towards, construction skills and and able skills as they are only 2 hours away from me. I'm based in Oxfordshire, I have 5 years background in...
  11. W

    Training Feedback Ardex Training Day

    I recently attended a large format tile training day run by Ardex, at their Haverhill trading centre. The day was very well organised and run by Andrea King & Vince Ruffini of Ardex, with support from Rubi - rail and cutting system. It was also a good opportunity to see and try some of the...
  12. Dan

    BAL Training Courses for Feb - Free for YOU+BAL users

    Just had this email and thought it'd be handy for BAL users perhaps. :) Up your game with BAL training Spaces Available on our February Courses At BAL we believe that quality workmanship is just as important as high quality products, which is why...
  13. Mapei UK Marketing

    Mapei Ceramic Training Dates 2020

    #Mapei #ceramic #training dates have now been confirmed for 2020. The day courses are FREE to attend and include a factory tour, refreshments throughout the day, a buffet lunch along & a goody bag. We can also offer dates for company & group bookings. For further info click here.
  14. Mapei UK Marketing

    Mapei 2020 Ceramic Training Dates

    #Mapei #ceramic #training dates have now been confirmed for 2020. The day courses are FREE to attend and include a factory tour, refreshments throughout the day, a buffet lunch along & a goody bag. We can also offer dates for company & group bookings. For further info click here.
  15. K

    Tiling course bristol

    Hi, anyone know of any good tiling courses in Bristol as I'm having trouble locating any. Thank you
  16. P

    Has anyone used silver trowel training academy?

    Evening guys, I’m very interested in a career as a self employed tiler, a company nearby (Lee on Solent) called silver trowel construction academy runs courses but before I part with cash I was wondering if anyone has used them before? I have done a fair amount of tiling but I know that there’s...
  17. LisaB

    Can anyone recommend a decent tiling course

    Morning. I'm new to this whole page & tiling. I'd like to do a tiling course & wondered if you guys have any recommendations? My other half is a plumber so I want to be able to help him out, grow & expand. I'm going to tile our ensuite & see how i get on. He can tile but he doesnt get time &...
  18. Dan

    Best Tiling Courses UK? -Recommended Tiling Courses

    Continue reading...
  19. D

    Just finished my tiling course! Go easy on me. :)

    Hey all. Hope you all been good. I just finished my tiling course . I am actually very excited about it. I been always adoring tiling. Not started yet. Having my CSCS course and test next week and hoping somebody will give me chance to to practice more . Kristine x
  20. Mapei UK Marketing

    FREE Event - Mapei Ceramic Products Training Course

    At Mapei we run training courses across various sectors of the construction industry. We meet all of your ceramic needs and requirements through our specialist ceramic products training courses. Our day courses are completely free of charge and held at our Mapei Academy training facility in...
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