Constructing semi-regular tilings of the plane with ruler & compass

Through discussion with fellow geometers, it seems there is a need for a simple resource showing the steps for drawing all eight semi-regular tilings of the plane using a ruler and compass, so I have compiled the methods presented here. There are, of course, many other ways to approach these tilings depending on your requirements. You can find sequential diagrams below, however if you enjoy print media or would like to support my work and help me fund further book projects, you can purchase a printed booklet version (with free UK delivery).

These tilings underpin many geometric patterns and are essential to understand if not always necessary to construct. If you need help constructing the hexagon and square you can refer to my earlier blog post about constructing regular grids with ruler and compass.

semi reg grid book

New published work

Some of my works have been published in the last month. Firstly, I have written a paper for the latest issue of the Journal of Illustration titled On the use of vocabularies of geometric forms in ornamental pattern design. This has been developed from a talk I gave at the Decriminalising Ornament – the 9th International Illustration Research Symposium and Exhibition at Anglia Ruskin Universiy in 2018.

As it is an academic publication, the cheapest way to access the article is pay per view of a single article for $14.

Secondly, some of my work has been featured in The Drawing Ideas Book by Frances Stanfield. “Refresh your creativity and boost your motivation to draw with the expert help of The Drawing Ideas Book.” Many thanks to Frances for including my work alongside many other great artists.

Art of Islamic Pattern Exhibition at Homerton Hospital

I’m very pleased to be exhibiting two painted geometric drawings as part of this group exhibition at Homerton University Hospital, London organised by Richard Henry and Adam Williamson from Art of Islamic Pattern alongside excellent and varied work in a range of media by a number of other geometric artists. If you would like to attend the private view from 6-8pm on 2nd July, please contact me.

Constructing grids with ruler and compass

In September 2018 I gave a presentation about patterns constructed using grids at the 4th International Workshop on Geometric Patterns in Islamic Art in Istanbul. For the presentation I prepared these timelapse videos demonstrating different methods for constructing grids using ruler and compass and I have posted them here to be of service to a wider audience.

Square and isometric (triangular) grids provide a rich and expansive foundation for the exploration of geometric patterns. They have arisen from the simplest regular divisions of the 2D plane. The triangle and the square are two of the three regular polygons which can tile a 2D plane by themselves. The hexagon is the third but can be seen as a combination of 6 triangles so equates directly with the isometric grid. These first two videos show the basic construction of the hexagon and square from the circle, fundamental constructions in the study of geometric art.


Timelapse geometric drawings for the Qatar National Library

Earlier this year the Qatar National Library opened a new permanent exhibition of artefacts from it’s Heritage Library collection. I was commissioned to make three timelapse videos demonstrating the construction of geometric designs featured in particular artefacts, to be displayed alongside the original pieces. In order to create the films I analysed and reconstructed the three designs and then produced these timelapse films demonstrating how the designs could have been constructed using the traditional tools of ruler and compass. It was an incredibly satisfying challenge which allowed me to incorporate a wide range of skills into one project.

The videos are currently on display the library and the exhibition also features books, manuscripts, historical photographs, maps, globes and travellers’ instruments that tell the story of Qatar, along with the history of science, literature, writing, travel in the region, and much more.


AV collaboration with Ali Wade

These are the fruits of an audiovisual collaboration between Ali Wade and myself. The music is by Ali taken from his recent album Geomorphology on the Frequency Domain label. The visual element is a shapeshifting collaboration of techniques between Ali and myself, combining freeform monochrome ink and chemical experiments with slow-moving geometric structures and transforming them into a tectonic whole.

Exploring geometric tilings with ruler and compass

blue-mosque-tilings-by-ambigraphInspired by Professor Miroslaw Majewski’s exploration of the pattern above left, seen at the Blue Mosque in Istanbul, I have developed a practical ruler and compass construction method which allows for the creation of a set of tiles which can be configured in numerous ways, giving rise to a whole range of patterns. Working through this method gives an insight into how a subgrid of regular polygons can underpin the construction of Islamic patterns and provide us with a key for the development of further patterns. (more…)