This is an ongoing journal of my personal explorations into the geometry of Richard Buckminster Fuller.
The following articles are arranged chronologically. An alphabetical list may be found in the sidebar. An index to the articles may be found here.
-
12-Strut Tensegrity Sphere and its Transformations
The 12-strut tensegrity sphere is the spherical, or tensor equilibrium phase of the the tensegrity octahedron and its dual, the tensegrity cube. Rectifications of either produce the cuboctahedron, i.e., vector equilibrium (VE) which serves as the template for the spherical phase. The sphere is transformed into the cube or octahedron by sliding the strut pairs… Read more
-
The Polar Pump Model of the Jitterbug
The polar pump model shows how the the jitterbug transformation might be conceived as the shuttling of nuclei along the primary axis of the 4 great circles via the octahedra they straddle. This is the same space-to-sphere, sphere-to-space oscillation as in all other models of the jitterbug, but allows us to visualize the transformation on… Read more
-
Blinkers, the Jitterbug, and the “Crystalized” Isotropic Vector Matrix
Implicit in the identification of any given sphere in the isotropic vector matrix as a nucleus is the categorization of every other sphere. Identifying a nucleus effectively “crystalizes” the matrix into three unique 13- and 14-sphere clusters of VEs and cubes I’m calling “blinkers.” As the matrix jitterbugs, these clusters generate patterns reminiscent of Conway’s… Read more
-
Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
The four sets of great circles and the 24 spin axes of the vector equilibrium (VE) are here discussed with regard to the radially close-packed spheres of the isotropic vector matrix.… Continue reading → Read more
-
Inter-Sphere Connections via the 25 Great Circles of the VE
The 4 sets of great circles and the 25 spin axes of the vector equilibrium (VE) are here discussed as the shortest-path geodesics between the radially close-packed spheres of the isotropic vector matrix.… Continue reading → Read more
-
Categories of Spheres in the Isotropic Vector Matrix: Nuclei, F1 Shells, and “Nuclear Voids”
When modeling the distribution of nuclei in the isostropic vector matrix, I distinguish between the nuclei and the 12-sphere shells that isolate and define them. These nuclear domains, each consisting of one nuclear sphere and a 12-sphere shell, defines the vector equilibrium, or VE. Nuclei are distributed throughout the isotropic vector matrix at the centers… Read more
The Geometry of Thinking 