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Picking up from last month and exploring further using the folds from last October I went deeper into reconfiguring the individual circles and using combinations I had not use in this direction of exploring open systems. Since the Pythagorean Theorem came up on one of the online math discussion groups I got sidetracked, then with traveling and conferences I had a short month.

Below is an account of my exploration, always looking for more clarity.

Two views of an open tetrahedron pattern but more like a truncated tetrahedron arrangement of four reformed circles. I have many reconfigured circles lying around that are of interest, but not having time or insight at the moment, they wait to be developed, or eventually to be discarded. This one is particularly lovely in its simplicity and economy.

Many of these formal arrangements do not fit the traditional classifications of geometric forms. The folded grid allow so many variations that fall between or outside of the few we have systematically classified

**Below** two views showing a variation using the folding from last October blog exploring the curving aspect of the folds. It has the symmetry of two open intersecting tetrahedra.

**Below** two views of fours circles in a tetrahedron arrangement. The one on the left has four open triangle planes, the one on the right the planes are closed. This system opens and closes as any system might with four, three-sided openings.

When open the form is stellated on all four sides using three elongated tetrahedra on each side.

Face view of the same system.

**Below** left shows a different reconfiguration where four circles are reformed and joined to form four open hexagon planes in the pattern of a truncated tetrahedron. To the right shows the open hexagons filled with another variation of the same folds making it a closed solid figure.

Here the above two systems have been combined. There are four different places and different combinations where one plugs into the other. This shows one of them that looked promising for continued development.

**Below** The above combination is expanded upon by adding elongated tetrahedra and other folded variations holding to a combined symmetry of three intersecting tetrahedra.

In another direction using the same folds in a different treatment of the tetrahedron pattern.

Here is a different variation coming from an octahedron center in a similar arrangement as the tetrahedron-centered model above. The individual units have been changed so it looks different. This shows a combination of two centered-related tetrahedra.**Below** is a variation where units have been added giving possibility for continued growth.

Here is another open tetrahedron arrangement of four circle in a very different reconfiguration from the same folds use above. Below layers are added using the same folded units except they have been reverse folded with inside to outside.

Seed

First layer

There were a number of other directions started but without time and clarity to explore further got put away. Sometimes months, or even years later I will see where something needs to go and then explore it further.

This is a an example of something interesting enough to sit around for a while that maybe I will figure out something about it. At the moment it simply is, and that is enough for now

Last month started with a continuation of the exploration over the last couple of months folding my business card circles. Here are a few things I explored before my attention got diverted towards preparing for workshops coming up on Orcas Island, WA and at the University of WA in Bellingham.

**Below** 3 views of four sets of three circles each arranged with an open center and then the sets joined in a tetrahedron arrangement showing an open centered system. Again these are all folded from reconfiguring the circle to the nine creases that come from folding the tetrahedron. There continues a deeper looking at the extraordinary transformational possibilities of the of the tetrahedron net pattern in the circle, not unlike what is observed with the stem cell.

**Below** Two views of another arrangement of four sets of three circles in tetrahedron arrangement

This open arrangement shows the forming that occurs on the inside

**Above** another view of three joined circles before the fourth was added, as completed above. We can see that the there is a beautiful almost coming together of the center points leaving a small tetrahedral gap when all four sets are joined.

**Below** More variations of four sets of three units where the centers are varied from open to closed.

Four sets of three with closed center arranged in a tetrahedron system where the inner points join at the center leaving the center open.

The same arrangement where the centers of each set have been folded over to form an open triangle center from the end point view.

**Below** I decided to use 9” paper plates to explore some of this in larger scale to see what the differences. Here two views of the same tetrahedron system of four sets of three circles each with an open center. The one on the right appears to have a floating cube which is in fact a plane perspective looking through the open center of one of the units of three circles.

**Below** two views of the same system with four more circles added expanding the form as it might in some biological growth. The appearance of the floating cube remains unchanged.

On Orcas Island I worked with middle school students in the morning and the high school students in the afternoon. There was good discussion with the high school students about the information and concepts that emerge from spherical compression and the first fold. The observable *principles* in that first movement clarify the structural forming of relationships observable in all kinds of disciplines, universal in application and directive to all subsequent folding. It is always gratifying to see students engaged in the math information and philosophical implications as well as seeing their excitement about the process of making things from circles. As often the case, and to my delight, a couple of students folded circles in ways I have not seen before.

Two days later I did a day-long workshop open to the public with people from Orcas and surrounding islands. Again there was also a good response from both kids and adults that also included a few teachers. It was the young people in the group that took the lead and explored beyond what others were still holding close. Again I observed reconfigurations that were new to me. People do not always reform the grid in the same way, they will explore different reconfigurations and systems that interest them. The connections that individuals make to what they are forming from the grid is often quite diverse, as was the case in the workshop in Bellingham a few days later.

There I worked with first year art students at the university. They had already done some folding of tetrahedra before we met. We explored folding the 8-frequency diameter grid. With that they moved into more complex folding and forming systems using multiple circles. As with most workshops, it challenged them to suspend their ideas about learned construction methods and traditional ways of art, to do from unity where nothing is added or taken away. Not so much about designing, rather observation, to see what is generated that stimulate the imagination. I notice art students are more product oriented, they do not work in groups the same way I see in other workshops. They do tend to explore more widely in reconfiguring the grid and experimenting with ways of joining.

While all three workshops were different, they all displayed the same excitement about what they were doing and new concepts they were discovering.