Jitterbug: Icosahedron as Maximum

By Greg -
Fuller described the "Jitterbug" transformation as the loss of the nucleus, causing the vertices to move closer to the center and creating the icosahedral shell. But if the vertices of the icosahedron are closer to the center than the vertices of the vector equilibrium, then why does it expand? The faces move closer together, but the vector equilibrium and the dodecahedron occupy the same, minimal, amount of space, and it's the icosahedron that occupies the most space. If Bucky didn't know this, it's surprising. But he didn't have access to 3D computer software. He only had his physical models.

From an isotropic perspective, the vector equilibrium does, indeed, appear to shrink during its transition into an icosahedron.

Jitterbug in VE phase -- Isotropic



Jitterbug in Icosahedron phase -- Isotropic

But from other perspectives, it's obvious that the icosahedron phase is the point of maximum expansion.

Jitterbug in VE phase -- parallel projection
Jitterbug in Icosahedron phase -- parellel projection.

It's a contradiction. The vertices do move closer to the center, but the cubic matrix expands numerically according to its frequency. If a single vertex moves x from the center, a matrix with a frequency of ten would expand ten-times-x from the center of the matrix. Individual contraction causing global expansion. Our bewilderment is an indictment of our models, of our 90-degree and up-down thinking.

Jitterbug in Icosahedron phase, with x = expansion factor

The expansion is due to the icosahedron's fundamental nature as a shell, rather than an all-space-filling poyhedron. The vector equilibrium at any frequency has the same number of layers as subdivisions. The icosahedron, at any frequency, is a single shell, and the interstices between closest-packed icosahedrons will always be irrational. It's the maximum dis-equilibrium phase of the jitterbug, which is in equilibrum (absolute zero) both in the "expanded" vector equilibrium phase, and in the "collapsed" octahedron phase. Curiously, the expanded and collapsed states take up equal space in the matrix.

Jitterbug in the equilibrium phase (VE-Octa)


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