← How these are made

Twelvefold quasi-periodic

شبه دوري اثنا عشري

Twelve-fold local symmetry with no repeating unit.

How it is made

The ground

The pattern is not drawn freehand onto the page. It grows out of this tiling — dodecagonal — which never appears in the finished drawing and decides everything in it.

dodecagonal

The contact angle

At the middle of every edge sits a point. Two rays leave it into the tile, each at the same angle from that edge, and run until they meet another. That angle is the whole parameter. This family is drawn between 45° and 58°, a range settled by eye.

45°
52°
58°

The numbers

Ground
dodecagonal
Symmetry
Quasi-periodic
Contact angle
45°–58°
Construction
Hankin polygons-in-contact

Sources

  • de Bruijn, N. G. (1981). Algebraic theory of Penrose's non-periodic tilings of the plane, I and II. Indagationes Mathematicae (Proc. Kon. Nederl. Akad. Wetensch. Ser. A 84). 43, 39–52 and 53–66.
  • Kaplan, Craig S. (2005). Islamic Star Patterns from Polygons in Contact. Proceedings of Graphics Interface 2005. pp. 177–185. read it

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