Seven sided sigils

As well as communing with nature, I like to explore sacred geometry. From simplicity complexity arises, and the complex in us can recognise that and see the simplicity within. The mind works with patterns, always searching for meaning, trying to find simplicity in the midst of complexity.

Here’s a simple idea – take seven points around a circle, and join them all together with a single line which visits each point once and once only. It turns out that there are exactly thirty-nine possible shapes. Here are some of the shapes –

Here is a star shape, nice and symmetrical


and here is a flying fish And there are other less symmetrical shapes like this one I call ‘raven on a throne’

There are patterns within the 39. They can be arranged into three groups of 13, and they can also be divided into 24 symmetrical ones (like the star and the flying fish, which are easy shapes for our minds to remember) and 15 asymmetric ones (like the raven on a throne, not so easy to remember).

There are complex and yet simple relations between them. The simplest relation is that of swapping two points. Swap a pair on one shape, and what other shape is the result?

Start with the three most symmetric shapes – which I call the three mothers…

Each of the three mothers has three daughters…

The daughters each have a son…

And all the children have fathers…

The first father’s children are the 2nd daughters, and the sons of the 3rd daughter. The second father’s children are the 3rd daughters, and the sons of the 1st daughter. The third father’s children are the 1st daughters, and the sons of the 2nd daughter.

If you put them all together, you get this shape (represented here as a flat picture, but really it curves back on itself to make a sphere.)

Complexity and simplicity. This reminds me of the patterns physicists think about for the underlying structure of the universe. For example see Garrett Lisi’s video on the Theory of Everything, and especially the animation which starts around 8 minutes in.


About singinghead

druid, mathematician, blogger, gardener...
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