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Miscellaneous

A miscellaneous, largely ‘for fun’ collection of various non in situ Cairo tiling aspects, in which the Cairo tiling is to be seen in a variety of mediums. The format is a picture and brief discussion. On occasions, I am unable to show pictures as the image holder did not respond to request for permissions, and where this arises I thus instead give a link.
    These all placed individually, broadly as found, rather than as a genre. Note that the compilation is of an ad hoc nature, of instances as found upon my researches, and therefore the collection, being in a permanent state of flux, is not particularly ordered in any way. Note that instances arising from the field of architecture, of which there are many, have been better judged placed as a separate page. The instances include: 

1. Polyhedrons (Jak Drinnan, Kenneth Peel)
2. Flooring (Forbo, First Base Pizzeria)
3. Shower Base (John Mansfield)
4. Tables (Andreas Hopf, Monzer Hammoud, Robicara)
5. Penta Graphene (Qian Wang)
6. Quilting/Patchwork (Josée Carrier)
7. Ceiling Panels (Tamara Restaurant)
8. Ironing Board Cover (Ikea)
9. Escher-like Tilings (Alain Nicolas)
10. Cushion (Macy’s)
11. Pavement Drawing (Pan-American Games)
12. Chairs (Bretzel Love, Monsieur Meuble)
13. Kimono (Moriguchi Kunihiko)
14. Canopy (Maple Square, Toronto)
15. Wine Racks (Grassi Petre)
16. Origami (Ron Resch, John Szinger)
17. Marquetry (Heliot and Co)
18. Exhibition Stand
 by Institute for Lightweight Structures and Conceptual Design (ILEK)
19. Wall Installation (Arndale Centre, Manchester, UK)
20. Acoustic Panels
21. 'Pentagonal framework' (Adriel Designs)
22. Board Game, 'Cairo Corridor', by Markus Hagenauer
23. Shelving unit, by Alexander Pincus, US

Does anyone know of other instances? Do let me know for inclusion.

Individual Listing:
1. Bisymmetric Hendecahedron, by Jac Drinnan
2. Flooring, by Forbo
3. Shower Base, by John Mansfield
4. Table, by Andreas Hopf
5. Quilting/Patchwork by Josee Carrier
6. Penta-Graphene Discovery
7. Escher-like Cairo tilings by Alain Nicolas
8. Tamara Restaurant Panels
9. IKEA Jall tabletop ironing board
10. Bow Tie, by Le Noeud Papillon, Sydney, Australia
11. Cushion, by Macy's, US
12. Flooring and Wall, First Base Pizzeria, Cape Town, South Africa
13. Pavement Drawing: Pan-American Games, 2015, Toronto, Canada
14. 'Bretzel Love’ Café chair, Paris, France
15. Torus, by Kenneth Peel
16. Kimono by Moriguchi Kunihiko
17. Canopy, Maple Square, Toronto, Canada
18. Chair, by Monsieur Meuble, a French furniture company
19. Wine Racks, by Grassi Pietre, for Zýmē Winery, San Pietro, Italy
20. Folded paper structure, 'Bar-Bell Yellow', by Ron Resch
21. Marquetry panels, by Heliot and Co, London, UK
22. Coffee Table, by Monzer Hammoud of Pont des Arts, Paris
23. Exhibition stand by Institute for Lightweight Structures and Conceptual Design (ILEK), of StuttgartGermany
24. Coffee table by Francesco Caracciolo di Marano and Sam Robin, with their company Robicara
25. Wall Installation, at Arndale Centre, Manchester, UK
26. Acoustic Panels, Norway
27. 'Pentagonal Framework', by Adriel Designs, US
28. Shelving unit, by Alexander Pincus, US
29. Origami, by John Szinger, US

1. Bisymmetric Hendecahedron, by Jak Drinnan


Another curiosity of the Cairo tiling is that it can be seen in an instance of polyhedra, specifically of the space-filling Bisymmetric Hendecahedron. Such a polyhedron is a relatively recent discovery, as reported in a 1996 paper by Guy Inchbald. For further details see:

http://www.steelpillow.com/polyhedra/five_sf/five.htm

Although the Cairo tiling as an entity was not directly noticed in Inchbald’s paper, an architect, Jak Drinnan, happened to notice this, and being familiar with the Cairo tiling made the association.

Although I am interested in polyhedra, this is very much secondary to my interest in tessellation. Indeed, I lack the mathematics here for a true mathematical treatment. Would any reader more familiar with this have anything to say?

For more on Jak Drinnan and the bisymmetric hendecahedron per se, see:

http://www.jd-d.co.uk/2012/07/material-designing-complexity.html

   


© Jac Drinan




2. Flooring, UK, 1950s Style? Natural Floors

A most interesting historical sighting, and in a ‘foreign’ context, is a sighting as a flooring, in the UK, of c. 1950s. However, details here are a little sketchy. A picture was posted on Natural Floors NW (North West) Limited website (and Facebook page) with an intriguing reference to the Cairo tiling in a bathroom of the 1950s:

https://www.facebook.com/Natural.Floors?fref=ts
However, upon correspondence with the company, the picture as shown is not the original flooring but is rather a modern-day recreation as best as is possible. Furthermore, the attributed date (the 1950s), is the best guess, from the age of the house and the material used, with printed tile effect linoleum. I quote excerpts from the company emails:
(Mail 1, 19 October 2015)
We had a customer buy a house built in the 1950's & in the bathroom was a printed tile effect linoleum, printed lino was a very popular floor covering in the UK from as early as the 1930's but the early ones were quite often floral patterns. As this house was from the 50's we assume the lino was of the same period. No one makes a printed lino anymore, (Vinyl is not lino!) so we made the [modern day] pattern by hand cutting sheet linoleum in 4 colours using Forbo Walton Linoleum as this was the closest we could get to the original colours.
and
(Mail 2, 20 October 2015)
We assume it is a 1950's pattern as this type of patterned linoleum was not made much beyond the 50's. Once vinyl became popular Marmoleum was used mainly in commercial locations. It is only now becoming popular again as a domestic flooring….
However, much still remains unknown here. Despite extensive web searching, who manufactured the vinyl, and what date these were installed is not known for certain, although 1950s does indeed seem a distinct possibility. Can anyone shed any more light on these background matters? Or indeed, have anything else to say on this?

   

© Natural Floors NW


3. Shower Base, by John Mansfield

An instance of a modern-day self-design is of bathroom floor at the home of John Mansfield, in North Potomac, Maryland, USA (about 25 miles north by north-west from the centre of Washington, D.C). This was built during the summer of 2014. The material is porcelain. The Cairo tiling was specially chosen for the project. John told me;
I wanted to do something mathematically interesting. I considered Penrose tilings, but in the small space of a bathroom it would be hard to appreciate that that pattern, though non-periodic, is not merely random. Plus I didn't like the look of that so much. Looking about tesselations, I came upon periodic arrangements of pentagons. I liked the interlacing of the two systems of hexagons. Building the floor with equilateral pentagons would allow an interesting geometric construction. 

© John Mansfield

4. Table, by Andreas Hopf

Some table designs as shown at design fairs, from Andreas Hopf, the designer.

http://www.hopfnordin.se


   

   
© Andreas Hopf



5. Quilting/Patchwork, by Josée Carrier

http://www.thecharmingneedle.com/2014/06/cosmic-voyage.html

© Josée Carrier


6. Penta-graphene Discovery

A recent development (February 2015) concerning the Cairo tiling is in the form of a scientific discovery, of ‘Penta-graphene’. Researchers at Virginia Commonwealth University (VCU) and universities in China and Japan have discovered a new structural variant of carbon called ‘Penta-graphene’ – a very thin sheet of pure carbon that has a unique structure inspired by the Cairo tiling. The newly discovered material is a single layer of carbon pentagons that resembles the Cairo tiling, and that appears to be dynamically, thermally and mechanically stable and can withstand temperatures up to 1,000 K (730 °C; 1,340 °F).

The background to discovery is relayed by one of the researchers, Qian Wang, Ph.D., a professor at Peking University and an adjunct professor at VCU, who was dining in a restaurant in Beijing with her husband when she noticed artwork on the wall depicting pentagon tiles from the streets of Cairo. 'I told my husband, "Come, see! This is a pattern composed only of pentagons,'" she said. "I took a picture and sent it to one of my students, and said, 'I think we can make this. It might be stable. But you must check it carefully.' He did, and it turned out that this structure is so beautiful yet also very simple."

The researchers' paper, ‘Penta-Graphene: A New Carbon Allotrope’, will appear in the journal Proceedings of the National Academy of Sciences, and is based on research that was launched at Peking University and VCU.

   

Restaurant image © Qian Wang


7. Escher-like Cairo Tilings, by Alain Nicolas

Some excellent Escher-like instances by the French artist, Alain Nicolas, based on the Cairo tiling. Other contributions are sought.

   

© Alain Nicolas


8. Tamara Lebanese Bistro Restaurant, Cairo

Some interesting and indeed novel use is to be seen at the Tamara Lebanese bistro, in Cairo, with numerous geometric patterned panels suspended from the ceiling, one of which includes the Cairo tiling. Such an instance gives credence as to its being a traditional Islamic tiling, although there is scant evidence of this. Upon enquiring with the company, of a Lebanese premise, on the possibility of these being from the Lebanon, they told me that these were simply generic Islamic designs.

   

© Tamara Lebanese Bistro


9. IKEA Jäll Tabletop Ironing Board

As drawn to my attention by Josée Carrier, and independently Robert Ferréol


10. Bow Tie, by Le Noeud Papillon, Sydney, Australia

Le Noeud Papillon, a bow tie company, of Sydney, Australia, has among their range two silk bow ties, of a pentagon theme, one of the recent (2015) Type 15 pentagon discovery, and another of a Cairo tiling. This is a limited edition of twenty, with a price of $165.

   
© Le Noeud Papillon Company


11. Cushion, from Macy's, New York, US
A cushion, available from Macy's, of New York, US, and other stores



12. Flooring and Wall, at First Base Pizzeria, Cape TownSouth Africa
http://retaildesignblog.net/2016/09/02/first-base-pizza-by-inhouse-brand-architects-cape-town-south-africa/

Another, so far unique instance, at least in combination, is that of flooring and wall tiles from First Base Pizzeria, of the Paddocks Shopping Centre, Cape Town, South Africa. This is a splendid sight indeed, of a multiple six-colouring, albeit without any apparent structure and appears to be of a modern-day installation, of 2016. This was designed by Inhouse Brand Architects, although the story behind its installation is unknown. Disappointingly, upon asking for picture permission and more details the architects did not respond, as well as a request to the (independent) photographer, Riaan West, hence the lack of pictures and more exact detail.


13. Pavement  Drawing, Pan-American games, Toronto, Canada

Pan-American games, Toronto, July 2015

14. 'Bretzel Love’ Café Chair, Paris, France

A ‘Cairo Café Chair’, as seen in Paris, France, from the ‘Bretzel Love’ Café chain. The background of this as to the designer and manufacturer are unknown. However, the chronology is roughly known; it appears to be ‘fairly recent’, the chain having opened in 2009. Of note is the interlinking structure, reminiscent of Rinus Roelofs’ work.
    With my thanks to Robert Ferréol, of France, for drawing this sighting to my attention.


© Robert Ferréol


15. Torus, by Kenneth Peel

The Cairo tiling realised as a 3D model onto the surface of a torus by Kenneth Peel, a student of mathematics at Bellingham, Washington state, US.
The file for making this is at:
http://www.thingiverse.com/thing:2001922/#files
And other instances, of further tori and polyhedra:
http://www.thingiverse.com/kennyp1369/designs

© Kenneth Peel

16. Kimono, by Moriguchi Kunihiko 

An interesting sighting, the first of its type, comes from the world of fabric/clothing, with a Kimono by Moriguchi Kunihiko (1941-), of Japan. This was a part of an exhibition on Kimonos at Paris in 2016 from November 16 to December 17, 2016, at the House of Culture of Japan to Paris. Kunihiko is a household name in Japan and has acquired a degree of fame, described as a ‘living treasure’ of Japan.
    With my thanks to Robert Ferréol, of France, for drawing this sighting to my attention.

© Jin Angdoo


17. Canopy, Maple Leaf Square, Toronto, Canada

A pentagonal tiled canopy (inspired by the experience of walking through a forest’s dappled light) by United Visual Artists (UVA) a London-based art practice, of a 90-metre long light sculpture spanning the front facade of the Maple Leaf Square building in Toronto, Canada, of 2010. Their form, abstracted from the geometry of leaves, reflect nature. Whether the designer was familiar with the Cairo tiling is unclear; it is not mentioned on their web page, and a mail asking for further details to UVA went unanswered. Of note in the panoramic view is the famous landmark the CN Tower in the background.

   
© James Medcraft


18. Chair, at Monsieur Meuble, a French furniture chain store

A unique sighting is of a chair, from ‘Monsieur Meuble’ a well-known French furniture store and chain of over 40 years old, with branches all over France. The chair appears to have been part of a liquidation sale. Does anyone know more on this? I have no other details.

© Vincent Pantaloni


19. Wine racks, by Grassi Pietre, for Zýmē Winery, San PietroItaly

An unusual, and indeed unique instance, is by Grassi Pietre architects, for Zýmē Winery, of San Pietro, Italy, with the pentagons used as series of wine racks, in stone, with the wine bottles stored in a vault in a cave, as temperatures must remain constant. The use of pentagons is predicated on the logo of the company, of a wine leaf in the broad shape of a pentagon. Each pentagon measures 78 x 56 x 60 cm and weighs 85 kg.

   
© Daniele Domenicali

20. Ron Resch - Folded Paper

Ron Resch (1939-2009) was a renowned artist, computer scientist, and applied geometrist, known for his work involving folding paper, origami tessellations and 3D polyhedrons. He famously designed the ‘Vegreville egg’, the first physical structure designed entirely with computer-aided geometric modelling software. Among his folding paper creations was a Cairo tiling, of a ‘folded mosaic’ titled ‘Bar-Bell Yellow’, possibly of 1963. 



21. Marquetry, by Heliot and Co, London, United Kingdom

http://heliotandco.com/surface-marquetry-cairo/
Another, so far unique instance, is that from the filed of marquetry, with real wood veneer panels from Heliot and Co, of London, United Kingdom. These retail at £255 for each square metre panel. This appears to be a modern-day appearance, of 2015.
    Disappointingly, upon asking for picture permission and more details the company did not respond, hence the lack of a picture.


22. Coffee Table, by Monzer Hammoud, Pont des Arts, Paris, France

http://www.pontdesarts.biz/
Monzer Hammoud, a Franco-Lebanese architect and designer, with his company Pont des Arts (founded in 2006), of Paris, France, a luxury interior design business of furniture and lighting, has an unusual instance of a coffee table top, of brass and marquetry wood, titled ‘Nexus’. Four of the pentagons form a par-hexagonal table. Note that the choice of design was no accident; Hammoud was familiar with the paving from living in Cairo for one year.

   
© Monzer Hammoud

23. Exhibition stand by Institute for Lightweight Structures and Conceptual Design (ILEK), Stuttgart, Germany

https://www.dezeen.com/2009/05/20/3d2real-by-ilek-students/
Another unusual instance is that of an exhibition stand, from the Institute for Lightweight Structures and Conceptual Design (ILEK), of Stuttgart, Germany. The stand, under the auspices of architects Werner Sobek, Fritz Mielert and Stefan Neuhäuser, was created to display the work of five young designers at design fair Blickfang in Stuttgart, in 2009.
    Disappointingly, upon asking for picture permission and more details the architects did not respond, hence the lack of pictures, although the link above discusses this in more than sufficient detail.


24. Coffee table, by  Francesco Caracciolo di Marano and Sam Robin, founders of Robicara company, US

http://robicara.com/galleries/pentagon-coffee-table/
Francesco Caracciolo di Marano and Sam Robin, with their company Robicara, of Miami, Florida, US, a luxury, high-end furniture business from 1997, has an unusual instance of a coffee table top, of individual elements based on the Cairo tiling, and of which can thus be assembled as a Cairo tiling, or of a looser arrangement if so desired. 

© Robicara 

25. Arndale Centre, Manchester, UK

Another unusual instance is that of a wall installation, at the Arndale Centre, Manchester, UK. However, so far, nothing is known as to the installation, beyond that it was this year, 2017. An unexplained feature is the largely randomised dark and light arrangement, without any discernable structure.
    My thanks to Tung Ken Lam for drawing this sighting to my attention.

© Tung Ken Lam

26. Acoustic Walls, by Kamilla Lang Hermansen

https://www.behance.net/gallery/273966/Pentagon
Kamilla Lang Hermansen, of Norway, a trainee architect at mmw architects (at least of 2008) together with the young designers at StookeAustad and the wood manufacturer Bosvik created what is described as ‘acoustic walls’. The walls were created for the exhibition at Beyond Risør in June 2008.
    Disappointingly, upon asking for picture permission and more details to Hermansen there was no response, hence the lack of pictures.


27. 'Pentagonal Framework', by Adriel Designs
http://www.charterworld.com/news/adriel-design-introduces-yacht-project-lumen-oceanco

An interesting, and unique instance, is of a ‘pentagonal framework’ interior, on the 90m luxury motor yacht ‘Lumen’, designed by Adriel Designs, of the US, an interior design firm, for the prestigious Dutch luxury yacht builder oceAnco, although the exact circumstances as to the installation are a little hazy. John Cantu, of Nautlis3D, is also seemingly involved in the project. Upon seeking more details, a mail to Adriel Design went unanswered, although Cantu responded. Unravelling the somewhat tortuous background with so many people and institutions involved is a task in itself, and of which I largely refrain from! This being so, the background details here are subject to revision. More details are given at the link above.

© John Cantu

28. Board Game, ‘Cairo Corridor’ by Markus Hagenauer
https://www.boardgamegeek.com/image/1566138/cairo-corridor

Another unusual instance is that of a board game, titled ‘Cairo Corridor’, by Markus Hagenauer, of Germany. This is commercially available, at Nestorgames, under the auspices of Néstor Romeral Andrés:
http://www.nestorgames.com/#cairocorridor_detail
And is described:
Cairo Corridor is a non-disconnection-and-area-control abstract strategy game for 2 players. In Cairo Corridor players alternate turns placing their pentagonal pieces in a board with a Cairo pentagonal tiling, trying to get the majority of pieces of their colour adjacent to a path that's being built during play and that connects the 4 sides.
The pictures show the game overall, in detail and Markus playing at the Nestorgames booth at Essen, Germany, 2013. (A major, annual four-day board game trade fair.)

      © Markus Hagenauer

29. Shelving Unit, by Alexander Pincus
https://pinc.us/cairo/

Alexander Pincus, an US architect, in 2013 designed a new series of steel and walnut furniture with the appropriately named ‘Cairo’ that explores a recurring hexagonal pattern. Elements include large and small display shelving, low cabinets, a credenza, and a room divider.

© Alexander Pincus

Origami, by John Szinger

Another unusual instance is that from the field of origami. This instance, of 2009, is by John Szinger, of the US, an authority on origami, with books to his name, notably Animal Origami Sculpture

© John Szinger

Page Created: 18 June 2012. Revised and enlarged subsequently

Overall page created 7 August 2014, for a more streamlined section, assembling previous single pages as a miscellaneous entity

10 November 2017. Format revised, as the scope was a little too broad, with three in situ Cairo tiling aspects included (Attraction, Manufacturer, Downtown sighting), now better judged placed elsewhere as entities in their own right.

2014
Quilting/Patchwork section added 2 October

2015
Penta-graphene discovery added 17 June
Natural Floors NW added 20 October
Escher-like Cairo tilings by Alain Nicolas added 9 November
Tamara Bistro Restaurant added 11 December

2016
IKEA 

Jäll tabletop ironing board added 5 January

Picture Links: Pan-American games added 6 January

Le Noeud Papillon, Sydney, Australia added 25 January

Cushion from Macy's department store added 28 January
'Bretzel Love’ Café chair added 8 September

2017
Torus by Kenneth Peel added 23 February
Kimono by Moriguchi Kunihiko added 9 June
Pentagonal tiled canopy, Toronto, Canada text and pictures added 14 July
Monsieur Meuble chair text and picture added 27 July
Grassi Pietre for Zýmē Winery, San PietroItalytext and picture added 28 July
Folded paper, by Ron Resch  text and picture added 26 October
Marquetry, by Helio and Co, London, UK text added 31 October
Coffee table by Monzer Hammoud, text and pictures added 3 November
First Base Pizzeria text and link added 10 November
Institute for Lightweight Structures and Conceptual Design (ILEK), of StuttgartGermany text and link added 13 November
Coffee Table by Francesco Caracciolo di Marano and Sam Robin, text and pictures added 14 November
Wall installation, at the Arndale Centre, ManchesterUK, text and picture added 15 November
Acoustic Walls, by Kamilla Lang Hermansen, of  Norway, text added 16 November
Pentagonal Framework, by Adriel Designs, text and picture added 21 November
Board game, 'Cairo Corridor, by Markus Hagenauer, text and pictures added 23 November
Shelving unit, by Alexander Pincus, text and picture added 30 November
Origami, by John Szinger, text and picture added 6 December 
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