Thursday, 23 August 2012 07:34

June, July Grows Into August


June’s exploration started in May and moved into July expanding into Aug before finding resolution. Each open leaf-like growth left from last month has become a closed bud-like form. This seems relatively stable as a model so I will leave it as such. Were it growing in the world it might well bring forth flowers that themselves would have seeds closed within, and so it goes. Through three month of development I have reached what appears to be the limitation of the material and the direction of the form of this model.


Below) Two views of present state.

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Below) Various stages of growth over the last three months starting with the tetrahedron and ending at the outer boundary of tetrahedra waiting for another season.

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Below) Details showing build up of last layer of tetrahedra folded from one crease in the circle.

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For instructions on how to fold a tetrahedron from one crease go to:

https://www.facebook.com/wholemovement/photos   and look for “Fold a Tetrahedron” and “One Fold Circle.”


This last layer of 115 circles, each folded to a tetrahedron using only one diameter crease, got me thinking about all I have seen revealed in one folded crease in the circle, the diameter. There must be much more that I have not seen. The vector equilibrium is fundamental to spherical packing and often the first model we make by joining four circles with three diameters each,  joining them on the straight edges. Knowing that curving the circle will reflect similar configurations that come from the folded triangular grid, it then seemed reasonable to assume the spherical vector equilibrium can be made using only one fold in each of the four circles. I reasoned since the first fold is a tetrahedron pattern and four tetrahedra in the same orientation sharing the same center point is the first centered system in the closes packing of spheres, called the vector equilibrium, traditionally the cuboctahedron. So I folded four circle one time and joined them together.


Below) The circle folded in half. Next is folding the diameter to itself dividing the circle into two cone shapes that are attached by the diameter fold. It is held together using a bobby pin.

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Above) Two circles with the diameter touching itself full length forms four cones, two sets of two cones each.

Below) To the left shows the two sets of two cones, two circles attached using bobby pins. To the right show the two sets of two cones each attached in the same way resulting in the spherical vector equilibrium. It is not accurate in circumference measurement from point-to-point (this can be achieved by moving the bobby pins to be equally spaced) but each point is equal distance to the center. This model shows the primary function of proportional triangular division inherent in the first fold of the circle. There are 6 square relationships between 8 cones pulled into triangulation.

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The vector equilibrium is the primary spherically centered system of twelve equally spaced spheres around a center sphere. This model demonstrates again the comprehensive, economical, and interrelated nature of folding circles, unique beyond all forms of modeling. What happens first in the circle is principle to all subsequent development. We have seen with the spherical model over the last three months, starting with one fold in the circle as a tetrahedron pattern of movement, and now ending with tetrahedra that are formed from one fold in the circle.

The next thing I fold will no doubt start with the same tetrahedron pattern of movement.  


(To see more about one fold in the circle go to http://wholemovement.com/blog/item/112-alignment-in-milwaukee





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