Some observations on the geometry of megakaryocyte mitotic figures: Buckyballs in the bone marrow

Mitotic figures in megakaryocytes are infrequent and those with
separated mitotic plates that allow for an examination of geometric
relationships are exquisitely rare. Nevertheless, over the years
images of 16N mitoses were collected; surprisingly, they did reveal
an underlying symmetry. In the 16N images (eg, Figure 1E), the
angles of the mitotic plates formed vertices of triangles, the
triangles formed tetrahedra, and the entire configuration appeared
to form a stella octangular (Figure 1F). This is an unusual
geometric composed of 2 tetrahedra one inverted and rotated 180°
with respect to the other. Although perplexing, the double tetrahedron
for 16N implied a single tetrahedron for 8N, and this was
confirmed with examples (Figure 1A-D). In an 8N cell, it seems the
4 centrosomes migrate to positions equidistant from one another as
they attempt to orchestrate anaphase. Four equidistant points on a
sphere form a tetrahedron

Anastasi, J. (2011). Some observations on the geometry of megakaryocyte mitotic figures: Buckyballs in the bone marrow. Blood, 118(24)

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Dense packings of the Platonic and Archimedean solids


Dense particle packings have served as useful models of the structures of liquid, glassy and crystalline states of matter, granular media, heterogeneous materials, and biological systems. Probing the symmetries and other mathematical properties of the densest packings is a problem of interest in discrete geometry and number theory. Previous work has focused mainly on spherical particles—very little is known about dense polyhedral packings. Here we formulate the generation of dense packings of polyhedra as an optimization problem, using an adaptive fundamental cell subject to periodic boundary conditions (we term this the ‘adaptive shrinking cell’ scheme). Using a variety of multi-particle initial configurations, we find the densest known packings of the four non-tiling Platonic solids (the tetrahedron, octahedron, dodecahedron and icosahedron) in three-dimensional Euclidean space. The densities are 0.782…, 0.947…, 0.904… and 0.836…, respectively. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other non-tiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. Combining our simulation results with derived rigorous upper bounds and theoretical arguments leads us to the conjecture that the densest packings of the Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This is the analogue of Kepler’s sphere conjecture for these solids.

Full paper

Torquato, S & Jiao, Y. (2009). Dense packings of the Platonic and Archimedean solids. Nature , 460(10), 876-879.

Dual Toroid Stuctures


“The dual torus topology occupies a central role in the spinor, twistor and quaternionic
formulation. This topology appears to be ubiquitous in astrophysical and cosmological
phenomena and is predicted by the U4
bubble of the affine connection in the HarameinRauscher
solution to Einstein’s field equations. The geometric structure of the complexified
Minkowski space is associated with the twistor algebra, spinor calculus, and the SU groups
of the quaternionic formalism. Hence quantum theory and relativity are related
mathematically through the dual torus topology. Utilizing the spinor approach,
electromagnetic and gravitational metrics are mappable to the twistor algebra, which
corresponds to the complexified Minkowski space. Quaternion transformations relate to spin
and rotation corresponding to the twistor analysis.”

Haramein, N., & Rauscher, E. A. (2007). Spinors, twistors, quaternions, and the “spacetime” torus topology”. International Journal of Computing Anticipatory Systems, D. Dubois (ed.), Institute of Mathematics, Liege University, Belgium, ISSN, 1373-5411.

Full paper.

Isotropic Vector Matrix (IVM)


To understand this, first consider again that the VE (and whole IVM) is the conceptual zero-phase cosmometry of the Unified Field. The Unified Field has an infinite energetic and creative potential. This potential is untapped until an impulse is introduced that causes the IVM to go out of equilibrium, and when it does so it “collapses the field” (as is often said in quantum physics when the consciousness of an observer seeks to determine the location or angular momentum of a quantum energy event) and an extremely minute amount of the Field’s infinite energy comes into a polarized dynamic of spin, differential, form and motion. A local energy event has emerged from the otherwise invisible and non-measurable Unified Field (a local energy event being something as basic as a photon, electron, proton, etc, and growing in complexity all the way to the macro scale of super-massive galactic clusters). Once a local energy event has arisen, a dynamic tension arises between its center point (its local “gravitational center”) and those in its near proximity as the contractive force of the collapsed field “pulls” on the surrounding field, and the center of each event tries to pull the others inward towards itself. When a stabilized system of such points arises, a geometric “tensegrity” form of energy is created.

The center point of each event can be described as the “singularity” around which the event is manifesting that remains connected to the infinite energy/density of the Unified Field. In this way, we can say that everything has a center point, and all center points are one (because they are continuously connected to the Unified Field’s IVM structure and therefore entirely and constantly unified). It is this unification of center points that explains non-local effects in the quantum realm that are proven to exist experimentally, wherein a change in the state of a quantum particle will simultaneously cause the same change in state of a paired particle across vast distances instantly (apparently violating the proposed cosmic “speed limit” of the manifest universe that is traditionally defined as the speed of light).


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