In order to build a periodic ornament, some methods are needed. Ernest Hanbury Hankin, Craig S. Kaplan, and Jay Bonner's methods are the reference techniques. In this article, we will go through the Hankin and Kaplan ones.
1- The Hankin method:
The first step consists of making an initial tiling. Then, the middle point of each side of the polygon is selected. From each middle point, two lines emerge forming an angle θ with the sides. Following that, the lines are extended until they meet each other for the first time. A second extension of the lines gives us another form.
2- The Kaplan method:
Kaplan used another approach by inserting a star pattern (star or rosette) inside the large regular polygon. In the second phase, he adorns the remaining patterns. Finally, he removes the initial tiling.
To sum up, Kaplan's method is based on the following four phases:
- (a) Making the Paving
- (b) Constructing the stars or rosettes to be inserted in the largest polygons
- (c) Adorning the remaining patterns
- (d) Removing the tiling