In late 90's early 2000's believed Gravity to be directly associated with the 5-fold icosa{20}hedron.
Via Bucky Fullers Synergetics we knew of know mathmatical way to commensurate the irrational 5-fold values, -- 1-around-zero{ none } sphere--,
with that of the rational 4-fold values of the Vector Equilibrium aka cubo-octahedron { 12-around-1 equal radius spheres }. My view was that, if could mathematically commensurate them, get closer to understanding Gravity.
Jim Lehman via a Pentagonal Vector Matrix, was able to create an all-space filling set of three kinds of polyhedra. there by mathematically with geometry, commensurate the 5-fold and 4-fold polyhedra.
1} regular icosahedron, in following graphic it is the orange polyhedron
2} six irregular 4-ofld octahedra, -- it is the pink polyhedraon-- and,
3} eight 4-fold polyhedra -- we called the Polycabin -- that is skew abberation of one of Archmedes 13 polyhedra, the rhombic cubo-octahedron. --it made clear with transparency show the tetrahedron inside of one of five of them.
Here is the Lehmanville graphic that only shows some of the actual arrangement that would fill all-space. It was only last few days I began to figure out more the minimal number of needed polyhedra to create this all-space filling set. Along with more specifics that I will post later on.
First here is the original roguh draft Lehmanville graphic Jim made.
For following me along with the numerical counting values, the viewer at some point, remove the orange icosaheron from considerraton and will need to see there is another beige icosahedron in this graphic and its as the central nuclear location between the four lower Popycabins where they and two of the pink irregular octahedron tangentally conjoin with 10 faces/openings of the central beige icosahedron.
More coming to better visualize the set of polyhedra, needed to be and all-space filling set.
