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equal parts, in the ratio of 1:2. Don't measure! Use your eyes, theyare made to see proportionally. Don't crease the folds yet.C. Fold unfolded part behind. Even up the points, straight andcurved edges. Crease only when the edges, points andcircumference are even. One fold on top, one in the middle, and one

on the bottom, like a "Z".D. This folds the folded semi-circle into thirds. Open to find 3diameters.

 These 3 diameters are a hexagon pattern of 7 points (6 end pointsof three diameters on the circumference and one center point of intersection). There are 6 equally divided intervals. The number forthe hexagon pattern is 13 (7+6=13). One circle and threediameters. Geometry is all about spatial patterns, the intervalsformed by the self-referencing movement of the of the Whole thatcreates endless reformations of organization.

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How To - page 5

Make an octrahedronA. Fold a tetrahedron.B. Open it half way so the triangular spaces are the same size asthe triangles that form them. There are 6 points and 8 triangularplanes; an octahedron pattern is formed from an open tetrahedron.

C. Make another tetrahedron and open it the same way. Join the 2opened tetrahedra, fitting the triangles of one into the triangleintervals of the other, joining edge-to-edge.D. Tape together along the full length of each joining edge. Thisforms the octahedron.

 The vector equilibrium sphere with triangles and square intervals,along with the tetrahedron (triangles) and octahedron (triangles andsquares) are three interrelated components to a single systemwhere all edge, surface, and interval relationships are congruent. There is much to explore using only these three units.

 The tetrahedron and octahedron are formed by 9 creased lines inthe circle, the tetrahedron folding. There are countless ways of reconfiguring and joining multiple circles using only these 9 foldedlines. The icosahedron is the next form to fold from the tetrahedron.

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How To - page 6

Make an icosahedronFold four tetrahedra, open them to flat triangles and arrange themreflecting the three triangles around the center forth triangle seen inthe single two-frequency triangle. Off set the three to the centertriangle by one half edge length (in the same direction forming aspiral) and taped edge-to-edge. This can be a left hand or right handspiral depending on which side of the center triangle you off set thethree triangles. Fold the edges together showing the same spiralpattern for each center triangle with the three spiral arms. Thisforms four triangle intervals (in a tetrahedron pattern) using 16triangles of four tetrahedra. Four triangles and one triangle intervalwill form a pentagon around each of the twelve points.

4 tetrahedron will make an icosahedron with 16 equilateral trianglesurfaces and 20 equilateral triangle planes. Keep in mind these arespatial patterns and form is simply the way patterns revealthemselves.

By completing the icosahedron, you will then have made the thirdprimary polyhedra of the five Platonic Solids by simply foldingtetrahedra. The other two, the cube and the dodecahedron, can also

be modeled by folding and joining tetrahedra, a stellation process of the first three polyhedra.

 This is the first step into the endless process of reforming theWholeness of the circle.

Gallery

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Here are pictues of 

more recent models

over the last four 

years. They are all

folded from 9" paper 

 plates. They

represent one

direction in

exploring the

 potential of folding

circles. The one

constraint I adhere to

is never cut the

circle. To do so

would be to destroy

the wholeness andlimit potential.

These are all

expressions of the

folded circle in

multiples to itself.

The circle is a total

self-referencing

system of 

 proportional

Wholemovement.

Left; some of the

shelving that line my

walls. These are

models I often use as

demonstrations.

Gallery - Page 2

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Above; 4 circles in a tetrahedron

 pattern.

Above; 20 circles in an

icosahedron pattern.

Below; 24 circles in a cube

 pattern.Below; 80 circles in an

icosahedron pattern.

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