Stars and polygons that fill a wall

This lesson asks you to identify the geometric properties of shapes that tessellate and the transformations that occur in tessellations. The museum offers one short card, on girih; the shapes themselves, the measuring of their angles and the transformations are for your class to bring. ¹

Look at a picture of a pattern of stars and polygons. Choose one shape, count its sides, and think about the angles that meet at each vertex. Then describe how one copy moves to the next: by sliding, by reflecting or by turning?

Yeomans sees the genesis of the Islamic arabesque in one style of Samarra stucco, where leaves and palmettes become abstract, lose their stems and are organised into the surface geometry of polygons and polylobes ². The style survives in the arch soffits of the Mosque of Ibn Tulun, where vine leaf, acanthus, palmettes and rosettes fill networks of interlacing circles, triangles and squares ^{3 4}. In Yeomans's view geometric forms in Islamic art are dynamic and open-ended, rarely coming to rest ⁴. The Encyclopaedia of Islam says two aesthetic rules are observed in the arabesque, and one is the wish to fill the whole surface with ornament ⁵. The records read name no designer of these patterns.

Both writers describe patterns that cover a whole surface. What is the difference between a shape that tessellates with no gaps and a pattern an artist chooses to spread over a whole wall, and why does it matter which of the two you are looking at?

• The arabesque: Yeomans's account of its birth, and the Encyclopaedia's principles of design.
• The Mosque of Ibn Tulun: where the stucco in the arch soffits survives.
• Samarran stucco styles: the three styles, one of which Yeomans sees as the genesis of the arabesque.
• Girih: geometric patterns of stars and polygons.

Read about girih. On squared paper, draw a polygon that tessellates with no gaps and name the transformation that carries one copy to its neighbour.