Building Physical Models of the Modular Units
Icosahedron As Outside Container
Dodecahedron Inside Icosahedron
To find the center of a pentagon divide 1/2 long axis by √3.618... and then divide again by GR. I found this configuration through a long process of trial and error. Now you can use it as a 'trail and error' tool.
These modular piece's calculations were involved. After finding the pentagon divisions we need the altitude of the dodeca-cone that builds the skeleton of the dodeca. That was calculated using the 90ËšTriangle Formula (Pythagorean theorem).
The rest of the measurements are a continuation of these procedures. Newtools color coordination of shape tells us what is constant.
Cube Inside Icosahedron
We start with the icosa using the 9.72326...cm edge. On the left are the numbers for the mass production grid for the orange bubble diamond.
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To accommodate the cube inside the icosa begin by constructing a half-size bubble triangle inside. Along one side mark the 1.90426...cm location and connect with the other corner.
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There is a left and right handedness to the icosa pieces. 4 corner units of the cube are one hand, 4 corner units are another hand.
There is a beautiful symmetry between the Sphere and Bubble families on the icosa division of the cube. The divisions of the square faces continue GR patterns we have encountered before, multiples of GR times Sphere family measurements.
The small triangle on the square face has the structural/numerical constants of the bubble triangle.
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We know the 1.62054...cm length, the others can be easily calculated. Know one know all self-organization.
Tetrahedron Inside Icosahedron
The modular pieces look complex but once you start building them their symmetrical logic is be revealed. There is a 3BB triangle inside the 6BB one. It's edge is divided into GR/ segments.
With a constant division of the outside corners giving us a place to start just connect to the locations-in-comon of the 3BB triangle edge.
Octahedron Inside Icoshedron
There is a change in size of the octahedron. The underlying order is all of the interior systems share locations-in-common with the outside limit of any container. In our original Platonic Solid nesting series the octa had an edge of 3BB to fit inside the tetra. Here, to fit exactly inside the icosa the edge is increased to . The octa shares 6 locations-in-common with the outside limit of the icosa. The smaller triangle inside is calculated by multiplying the edge of the larger triangle by .
The Bubble Triangle of the icosa has an edge of 9.72326...cm. If you multiply that length by GR you get the edge of the smaller triangle inside the octa with edge of 11.12461...cm. The other divisions are related to the edge of the octa.