division
unit repeat
How to divide a polygonal pattern into a second layer?
We’ll illustrate with an example. Below you can see a typical pattern with a 10-pointed star, surrounded by pentagons and rhombuses. The unit repeat is drawn in red.
![Image](https://beta.geogebra.org/resource/rcmmevpk/tIyDDnakjlzywzcp/material-rcmmevpk.png)
dividing the unit repeat
You can create a division a follows:
- Construct regular decagons at the corners of the line pattern so that they are tangent. Below you can see that two decagons overlap. For this an alternative is provided.
- Fill in the remaining area with polygons of the 5-fold system. The overlapping decagons are replaced by bow ties and hexagons.
![Image](https://beta.geogebra.org/resource/kuntynma/0esPTGtqD2S15LmA/material-kuntynma.png)
We duplicate the divided unit reapeat by mirroring.
![Image](https://beta.geogebra.org/resource/djwbqtp9/5MROxyHd2ySUPLzB/material-djwbqtp9.png)