PCAPPC

The Jitterbug transformation can be reduced to the rotation of a triangle inscribed in a cube. If the rotation is constant around the vector described by the cubic diagonal, and the triangle's vertices are constrained to follow the x, y, and z planes defined by the cube, the triangle will move along the vector in an inverse-square relationship to its rotation. Consequently, the jitterbug seems to "bounce" between phases. Eight triangles, four rotating clockwise and four rotating counter-clockwise, comprise the jitterbug which collapses into a regular octahedron with each "bounce." The three phases of the jitterbug transformation are associated with three polyhedra. The first is the cuboctahedron, or truncated cube, which Richard Buckminster Fuller called "the vector equilibrium." All vectors, both the edge vectors and radial vectors, are the same length, and may thus be thought of as the vector representation of the closest-packing of equi-rad...

I used the programming language, Ruby, and SketchUp Make 2017 ® to create the following animations demonstrating the geometrical transformation known to its discoverer, Richard Buckminster Fuller, as the Jitterbug . The jitterbug transformation is typically modeled as hinged vectors and rotating triangles. But as the vectors are meant to model the joining of sphere centers, I've here replaced the vertices with spheres. The doubling up of edges at the octahedron phase of the jitterbug is here represented by merging and diverging spheres. Different views and rotations reveal some interesting characteristics of the transformation. If the view rotation is synchronized with the rotation of the top and bottom triangles, the transformation resembles a pump with spheres orbiting around its equator. A different angle and without rotation, the spheres merge and diverge at right angles. Finally, the conventional view of the jitterbug, with its synchronously rotating triangles replaced...