The winner of the competition is José Bradamonte. He handed in a hand-drawn hexagonal solution with a weaving and slightly curved lines. Congratulations José!
This solution clearly shows the symmetries of the pattern: Threefold rotational symmetry around both the big and the small sixpointed stars and reflection symmetries in three directions.
This pattern belongs to a newly discovered category of patterns that belongs to a wallpapergroup that was very scarcely used in Islamic design.
More variations I will publish soon.
Here is a part of a tessellation consisting of sixpointed stars (two sizes), fivepointed stars, hexagons (three types which have almost equal shapes) and, in the middle, a tile with the shape of an incomplete star and a hexagonal empty space in the middle.
With these seven different tiles the plane can be tessellated.
Try to find it!, by printing the pdf file below and expanding it using these seven tiles only.
If you find the solution, draw it, color it and send a picture or scan before 1 july 2014 to email@example.com.
Those who send the most beautifully decorated, correct solutions win a special prize!
(This competition was won by José Bradamonte, his solution is shown above)
Dit is een deel van een vlakverdeling die bestaat uit zespuntige sterren (twee groottes), vijfpuntige sterren, zeshoeken (drie types die bijna gelijke vormen hebben) en, in het midden, een tegel met de vorm van een onvolledige ster met een zeshoekige open ruimte in het midden.
Met deze zeven tegels kun je het hele vlak vullen.
Probeer de oplossing te vinden door de pdf hieronder te printen en vervolgens uit te breiden met alleen diezelfde zeven tegelvormen.
Kleur je oplossing in en stuur een foto of scan naar firstname.lastname@example.org.
Wie de mooist versierde, correcte oplossing instuurt wint een bijzondere prijs!
(De wedstrijd is gewonnen door José Bradamonte, zie zijn oplossing hierboven)
P.S. An advice: Use tracing paper (overtrekpapier of patroonpapier) to find the solution. Success!
These patterns were designed with the use of drawing in a 16th century manuscript. In this drawing, a subgrid consisting of two types of hexagons is used resulting in a pattern with regular heptagons. I made use of the same subgrid to design patterns with regular octagons. (feb 2014)
This tessellation suggests the possibility of combining these various 'perfect' stars in this way. However, the stars aren't exactly regular! There are small imperfections making this combination possible.
Mathematically speaking: The 16-pointed stars do not have an exact 16-fold rotational symmetry and the 7-pointed stars do not exactly have 7-fold rotational symmetry.
These types of mosaics, with slight irregularities were produced in the Seljuk period (11th-13th century Persia) also. Mr Peter Cromwell wrote an article about this, to be published in 2014.
Two students Daphne de Ridder and Thomas Mast from Texel who did the course on Islamic patterns won the Texel 2012 design competition. Their work is reproduced electronically in triplex. Therefore I drew their design using 'Geogebra'. The result is shown here. The colourful end result of the students (They called their work 'Lente', meaning 'Spring') can be found at leerlingen presenteren hun werk.
The pattern has a typical Persian style and it wouldn't surprise me if the design was made before during the middle ages in the Persian region thus making the student's design a 'reinvention' of a pattern designed centuries ago. Its basic pattern consists of squares, hexagons and dodecagons hence the many four-, six- and twelvefold local or total rotation symmetries.
Here's a photograph of the mosaic in triplex. I published a series of photo's showing the production process at van leerlingontwerp naar kunstwerk.
With the drawing programme 'Geogebra' I designed this Persian-style pattern with regular eight- and ninepointed stars. The pattern has reflection and glide reflection symmetries, four- and twofold rotational symetries and local eight- and ninefold rotational symmetries. Besides the two starshaped tiles there are three other types of tiles. Two of them have one axis of symmetry, the third one has two axes of symmetry.
For information about the design technique used and in case you wish to use this design for any goal, please contact me.