Tenfold Pattern Variations

As many of us enter a period of isolation in the unusual and unsettling situation the world finds itself in, many of us will take the opportunity to spend time learning new skills, a process which can help us both focus and relax at the same time. For me, these qualities have been invaluable ones to develop and geometry has played a central role in this development. The process of drawing geometric designs with ruler & compass can help you find your own centre much as we start drawing a geometric pattern by locating the centre of the first circle, which then defines the structure of the whole pattern. Everything is grounded in this point, as we are grounded in our own centre.

Since becoming immersed in Islamic geometric design I have found myself drawn to overlapping rosettes which appear in a number of forms, particularly within tenfold patterns. This design is slightly unusual as it repeats in a hexagonal unit and the main star or rosette centres are defined by this hexagon rather than the repeat rectangle. I hope you will find this an enjoyable and enlightening construction to spend some time with.

Start by constructing a circle divided into ten. You can find steps to do this in this tutorial and various other places online. Continue with the steps below which show how to establish a repeat rectangle with centre and corners divided into 20ths (18º).

Overlapping tens - Ambigraph Mar 2020_Page_02
Overlapping tens - Ambigraph Mar 2020_Page_03
Overlapping tens - Ambigraph Mar 2020_Page_04
Overlapping tens - Ambigraph Mar 2020_Page_06
Overlapping tens - Ambigraph Mar 2020_Page_07
Overlapping tens - Ambigraph Mar 2020_Page_08

This is a very important base layout and a multitude of tenfold patterns can be constructed from this starting point. Here are three related variations.

For the first two patterns, we need to add some extra circles and divisions as described in the steps below. I have highlighted the basic repeating hexagon in the last slide.

tenfold hexagon repeat R&C-01a
tenfold hexagon repeat R&C-01b
tenfold hexagon repeat R&C-01c
tenfold hexagon repeat R&C-01e
tenfold hexagon repeat R&C-01f

From this layout, although I haven’t outlined every step, you can complete the pattern using existing intersections.. it may take a little comparison between my diagrams and your drawing to see the required connections. The same layout of circles and divisions will yield the two patterns below and, for the explorers among you, perhaps more to discover.

Starting again from the base layout of the rectangle and 1/20th divisions we can go in a different direction to construct a related pattern using different angles and a different vocabulary of shapes. Follow the steps below to establish circles and divisions.

tenfold hexagon repeat R&C-01i
tenfold hexagon repeat R&C-01j
tenfold hexagon repeat R&C-01k
tenfold hexagon repeat R&C-01l
tenfold hexagon repeat R&C-01m

… and the pattern itself.

tenfold hexagon repeat R&C-01n

I hope you enjoy exploring these patterns and that it may lead to your own insights and discoveries. If you post your drawings on Instagram, please tag me @ambigraph so I can see your work. Finally here is an alternative tiling of the repeating hexagonal unit with a jaunty rhythm.

6 Responses to “Tenfold Pattern Variations”

  1. Sidraj

    Soooo beautiful and difficult as well … as it will be my first to try hands on such art
    But soon try …. love it though

    • ambigraph

      The first circle proportions slide shows how to establish the radius. You then draw the 6 circles in the second slide which are centred where the larger circles cross the verticals.


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