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