Excavated dodecahedron – complete

Finally managed to finish the excavated dodecahedron!

First I made another six pentagonal units.

excavated dodecahedron work in progress

Then I stitched them together to form the second half.

excavated dodecahedron work in progress

Then I joined the two halves to form the complete dodecahedron.

complete excavated dodecahedron excavated dodecahedron

It is a little wonky – it was tricky to get all the pentagonal units exactly the same size. And some of the joining could have been neater, though it was tricky making the final joins, as I had no access to the needle on the back side.

But I’m pretty pleased with it as a proof of concept. 🙂

Geometry in Iranian art

iranian geometry3

In my travels, I’ve often been awestruck by the dazzling geometry of Islamic art, seen in Mughal architecture in India, Turkish mosques, and the Alhambra Palace in Granada, to mention just a few examples.

So as a break from the production cycle of felt and indigo scarves for the upcoming slew of Christmas markets, on Saturday I attended a workshop on geometry in Iranian art at Kensington and Chelsea College.

The tutor was Amber Khokhar, whose beautiful ceramics I saw and admired a couple of years ago at her studio at Cockpit Arts in Deptford. Amber gave a short presentation showing some examples of geometry in nature that have inspired geometers throughout history.

But most of the time was spent working on our own geometric tessellated patterns, using ruler, compasses, set square and pencils.

The type of pencil is crucial – we used H or F pencils for marking the initial grids, and B pencils for drawing the final lines. Pencils must be sharp – Amber uses a nail file as well as traditional sharpeners to hone the point. And because accuracy is super important, she told us to keep the pencil upright rather than at an angle when drawing so that the line was as thin as possible.

Perhaps surprisingly, the only time we used the ruler for measuring was to set the radius for the compass – in this case 7cm. Otherwise, all the points of intersection were created using the compasses, and the ruler was used only as a straight edge to join up the points.

All designs start in a similar way. We drew a vertical line (connecting heaven and earth) and then drew a circle on the centre of the line. Then, by adding a series of arcs, we ended up with a square containing four “petals”. From this, by adding more diagonals and/or more squares, we developed several different patterns.

Two of these we developed to full tessellations, covering a sheet of A3 cartridge paper, by tracing the original pattern and using it as a kind of stencil.

The first design is known as “the breath of the compassionate”, a combination of four-point and eight-point stars.

iranian geometry1vandatiles

I’m not sure whether the other pattern had a name, but the main repeat pattern was based on an eight-point star (some of the lines are a bit faint as I haven’t yet gone over them with a B pencil). I haven’t been able to find an example of this pattern in real life, though I’m sure one exists.

iranian geometry2

It would have been interesting to colour in some of these patterns to help them come to life, but unfortunately the college had not left out the requested materials. (This was not the only poor piece of organisation – there was confusion over the starting time, resulting in half the class arriving at 10am and the others at 11am. It made things quite difficult for Amber, who essentially had to run two different classes for part of the time.)

Tracing out these repetitive patterns was strangely soothing, I found. However, this was only on an A3 sheet of paper – the patience and accuracy required to reproduce such patterns, say, in ceramic tiles over a much larger space is admirable, to say the least!

If you’re interested in reading more, this site gives some useful background as well as explaining the geometry behind common patterns.