Structural Interconnectedness
Synergy of Parts
Building Physical Models of Interconnectedness
If you have explored the first three portals you have all the tools necessary to investigate fundamental structure looking for a new understanding of structural integrity. When a load is placed on a structure, the more structural integrity it has the greater the ability to 'communicate' that load over the entire structure increasing its strength. Whole systems thinking means you are always looking for how the integral parts are connected into one synergetic whole. We will begin with the simplest communication network inside the Five Platonic Solids; connecting their centers to their outside corners.
The Skeletons of The Five Platonic Solids
I call the lines of communication between a system's center and its outside corners a skeleton because it is the foundation of the modular division of the volume of a system. The other networks are relative to this.
Icosahedron Skeleton
The color coordination of shapes tells us useful information of each shape. In this example, the structural and numerical constants of the orange bubble diamond are relative to the icosahedron in the nesting series. A diamond is a shape with 4 equal sides with an internal order of a long axis and a short axis.
Here is the self-correcting mass production grid for the bubble diamond. You begin by measuring the 'where' lengths (vertical) and then the 'when' (horizontal) to make a rectangular grid. Each shape has its unique method of laying lines of communication between locations-in-common. (See Basic Tool Kit portal).
Axis of Spin-in-Common
Cube's Axis of Spin
The axis of spin for these 4 systems above are the same, √6(1.5BB) = 7.34869...cm. The skeleton of the cube tunes them all. How geometrical systems contain each other reveals the underlying interconnectedness of all fundamental systems.
Cube Skeleton
We are exploring the skeleton of the cube now because these numerical constants 'tune' many of the other communication networks in the Five Platonic Solids.
The color green tells us this is a sphere diamond and divided along its short axis gives us what I call a sphere triangle. The dimensions of the 90Ëštriangle of the sphere diamond define a numerical constant that interconnects the icosahedron, dodecahedron, cube and tetrahedron, √6(1.5BB) = 7.34869...cm.
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When you multiply square roots you simply multiply the numbers inside the symbol, √2 X √3 = √6. This number √6(1.5BB) along with the 90ËšTriangle Formula (Pythagorean theorem) helps us calculate the other constants.
The sphere diamond self-correcting mass production grid begins with the rectangular grid. The lines of communication begin with connecting opposite corners of the tall rectangle across the page. Next, connect the corner to the midpoint across the page. This will divide the edge of the sphere diamond into 1/3 segments. This will be helpful in building the smallest modular unit in basic geometry, Fuller's 'a' and 'b' mods.
Dodecahedron Skeleton
To mass produce this cone shape is very straight forward. We know the long side is our number-in-common 7.34846...cm. The 6.87538...cm length is calculated using the 90Ëš Triangle Formula because we know the top number is 5.24419...cm.
Using 6.87538...cm as 'where' and 5.24419...cm as 'when' you can mass produce this shape. With 3 rows you can describe the center line by connecting locations-in-common.
Tetrahedron Skeleton
The skeleton of the tetrahedron is built from the sphere diamond but this time the shape is divided in half by its long axis. We will see the tetra and the cube has many connections.
Octahedron Skeleton
What we will find over and over is the interconnectedness of the octa, tetra and cube. Here the square is divided into 4 equal parts that form the skeleton the octahedron.
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The self-correcting mass production grid combines the where/when measurements into one number to draw out the grid.
Icosahedron Inside Octahedron
