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In the last article we saw that individual galaxies grow along geometric lines and this geometry can be seen as a cross-section of Platonic solids, Compound solids and their duals.  We will now see that not only are individual galaxies structured along geometric lines, but galactic clusters are as well.  We will review and expand on Conrad Ranzan’s work here from Article 35 regarding the Cosmic Cellular Structure of the Universe.



Geometry of Galactic Clusters

We have seen from Dr. Harold Aspden how each sun sits in the center of a solar domain.  These solar domains are cubic in nature (or possibly octahedral).


On the galactic clustering level, these domains are rhombic dodecahedral and rhombic-trapezoid dodecahedral.

Rhombic Dodecahedron.  Credit: Conrad Ranzan



The Cosmic Cellular Structure

There are three ways in which a volume can be divided into ordered polyhedral cells.

This means the cells are identical units and there are no gaps between each cell.  They will tessellate.


  1. Hexahedra (cube) (Platonic solids) – unstable when subjected to forces involved because the corners are farther from the center than the sides. This creates an unstable shape.


  1. Truncated octahedra (Archimedean solid) – surface-to-volume ratio 5.31
    1. Surface tension cells, striving to maintain their volume and surface area take this shape.



  1. Rhombic dodecahedra (Catalan solid) – surface-to-volume ratio 5.345
    1. Negative pressure cells, striving to maximize their volume and surface area take this shape.


Cosmic cells are negative pressure cells – negative pressure is the manifestation of the process of aether expansion.


*Note – the rhombic dodecahedron is dual to the cuboctahedron!

The cuboctahedron

The rhombic dodecahedron

The cube-octahedron is the seed-shape of the space medium (Aether) according to Buckminster Fuller and Nassim Haramein.  It is the ‘ground-state’ geometry since it is the most stable shape of all besides the sphere.



Voronoi Cells

“In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells.”1

Wikipedia tells us that, “Voronoi tessellations of regular lattices of points in two or three dimensions give rise to many familiar tessellations.


In earlier articles we saw how Voronoi cells and DeLauney Triangulation created the cellular structure that we see in plants, animals, insects and animal wings.


Now we will see how they play a part in the cosmic cellular structure of the universe.



Geometric Centers of Expansion (GC)

The assumption is that all the GCs have the same capacity for repulsion and are free to move about.

On a 2D plane, one of the distributions of GCs reveals a square cell and the other, a hexagonal Voronoi cell.

Intuitively we know that the hexagonal pattern will be the natural outcome of the repulsive force.


With the hexagonal pattern, the GCs fulfill their goal of maximizing distance which increases by a 1.075 factor without any change in the total area of its domain.

By using 3D Voronoi cells with the rhombic dodecahedral shape instead of the hexagonal shape, the distance between geometric centers is greater by a substantial 12.25 %.


It appears that our Universe is structured as Voronoi cells and the shape of the structures is predicted to be dodecahedral.

This has been backed-up by the discovery of large-scale structure in the universe by several scientists.  We will discuss them in more detail in the next article.


British mathematician Ian Stewart writes, “Now the Voronoi cell is a polyhedron.  Astronomers have recently discovered that the large-scale distribution of matter in the universe resembles a network of such polyhedra. Most galactic clusters seem to be located on the boundaries of neighboring Voronoi cells. This pattern has been called the Voronoi cell model of the universe.”

Credit: Conrad Ranzan


Science writer Timothy Ferris writes, “In the 1980s it was discovered the clusters of galaxies are organized into giant bubbles measuring some 300 million light-years in diameter…And preliminary research indicates that the bubbles do indeed represent the top level of structure.”



Lambda and Gravity – The Heartbeat of the Universe

Conrad Ranzan explains,“On the largest structural scale Lambda manifests itself as the interior void of a bubble-like cosmic cell.  On the grandest scale of all, Lambda (expanding Aether in conjunction with contractile gravity) manifests itself as the Cellular Universe.

Credit: Conrad Ranzan


Space expansion (generic Lambda/expanding Aether) acts as a repulsion force that strives to maximize the distance between centers of expansion.  These geometric centers represent the centers of the voids from which space expands.  And they act like centers of anti-gravity, from which precipitating matter is conveyed outward.

As the space inside the cells expands, star clusters and galaxies and other matter become concentrated along the common Voronoi boundaries.

(This is how we see growth occur on every scale.  As the entity expands – that is, grows and evolves – regardless of whether it is an electron, insect, plant, human body, planet, galaxy or galactic cluster, it’s matter becomes concentrated along geometric boundary lines.)

Cymatics patterns.  Sound (Vibration) creates geometry.  The colloid particles (or photons) are attracted to the lines of force – the geometric boundary lines.


Lambda is on the inside; gravity (and mass) is on the outside!  Gravity prevents Lambda from enlarging the cosmic cells; while Lambda prevents gravity from collapsing the cells.”2

Credit: Conrad Ranzan


Remember, though, it is all Aether.  Aether expands (Lambda) and contracts (Gravity) and these are the different forces being discussed.



Remember Dewey B Larson & Large-scale Structure of the Universe

Local Space Expansion (Radiation)

Every location in the universe is moving outward from every other location at unit velocity because of the space-time progression resulting from the equivalence of the basic units of space and time.


Local Space Contraction (Gravity)

Simultaneously all material atoms are moving in the opposite direction, inward toward each other, because of their rotational motion. (Gravitation)

These motions control the large-scale aspects of the material universe.

(This outward/inward expansion/contraction is represented by the torus, which exists at all scales.)



The Cells Do Not Expand!

Please note – It is not a universe where cells are seeded and then grow to maturity – it is a universe in which cells are merely sustained.

The cells simply exist as timeless patterns and are maintained by perpetual steady-state processes.  The cells are not ‘things’.  They are Aether flow processes.  It is the process that creates and sustains the cells which themselves are invisible to us.

It is a Dynamic Steady-state Universe (DSSU).  It is ever-changing within a static framework.

The cells do not expand – they are prevented from expanding by a self-balancing mechanism resulting from Aether flow (centripetal/centrifugal).

The DSSU cosmology has long predicted that the Universe is a tessellation of Voronoi cells in the shape of dodecahedrons.  In the year 2015, a revolutionary paper was published in which the shape of the observed cosmic cells was verified to be dodecahedral.”3



Large Scale Galaxy Structure

Stephen Gregory and Laird Thompson write, “Clusters tend to lie close to one another…and the voids are evidently an integral part of the process of clustering and superclustering.”4

“Since expansion is radial, matter will co-move with space in an explosion-like pattern. In effect, matter will free-fall towards the outer boundaries and into the interface region, a region of aggregation. Each cosmic cell, in this manner, is accreting the material not only from its own interior but also that from the twelve (eighteen, more correctly) surrounding neighboring units.

Any galaxy cluster that astronomers term “filamentous” is the tracing of one or another of such boundary lines or edges.

Sheets of galaxies, filamentous clusters, dense concentrations at nodes, and large voids are all features predicted by DSSU theory.  The observational evidence is an overwhelming affirmation.

Astronomer Jaan Einasto had found that the large scale organization of galaxies does have a net- like cellular structure with interconnected strings of galaxies surrounding empty regions.

Laird Thompson and Stephen Gregory found that galaxies were never isolated but appeared to be joined to larger structures in chains or filaments with empty regions in between.”5


In other words, “The large-scale structure of the Universe is made up of voids and filaments, that can be broken down into superclusters, clusters, galaxy groups, and subsequently into galaxies.

Although there are some galaxies that are found to stray away by their lonesome, most of them are actually bundled into groups and clusters. Groups are smaller, usually made up of less than 50 galaxies and can have diameters up to 6 million light-years. In fact, the group in which our Milky Way is a member of is made up of only a little over 40 galaxies.

Generally speaking, clusters are bunches of 50 to 1,000 galaxies that can have diameters of up to 2-10 megaparsecs. One very peculiar property of clusters is that the velocities of their galaxies are supposed to be too high for gravity alone to keep them bunched together … and yet they are.”6

Here is where mainstream science throws the ad hoc concept of ‘dark matter’ to explain how clusters remain together.  In Cosmic Core we know that ‘dark matter’ = Aether.

Journalist Adam Hadhazy writes, “Once thought of as uninteresting backwaters, voids are emerging as the new big thing in several realms of astrophysics. ‘Voids are a comparatively young field, but people are excited,’ says Bhuvnesh Jain, a professor of astrophysics at the University of Pennsylvania. Because of their profound emptiness, voids make unique laboratories for testing why the universe looks and behaves the way it does. Astronomers can study voids to tackle the cosmological bugaboos of dark matter and, in particular, dark energy.

“Voids are the best place to look for the signature of dark energy,” says Vogeley. If those signatures never turn up, voids might instead put the kibosh on dark energy, ushering in new forms of gravity or even a new force of nature. If all that weren’t enough, studying those rare, loner galaxies that call voids home should shed light on how all galaxies evolved over the universe’s eons.”7

Let the ushering in of new forms of gravity begin!  The new scientific paradigm is knocking at our door.  It is time to let it in.



Cosmic Building Blocks

Jeremiah P. Ostriker writes, “The bubble interior would be a void, but the bubble wall would be the site of vigorous activity.”


The ideal Voronoi shape and the ideal cosmic cell is the rhombic dodecahedron (pictured below).


However, Nature, on her grandest structural scale in physical reality, has an asymmetry and possibly random flaws as well.


Cosmic bubbles may take the shape of either the rhombic or the rhombic-trapezoidal dodecahedron.

Rhombic-trapezoidal dodecahedron


Tessellating Rhombic-Trapezoidal dodecahedra


The DSSU is an infinite array or lattice of such shapes.

The shape of the cosmic cells is determined by the Voronoi principle.

The size of the cells is determined by the equilibrium between the rates of expansion and contraction.

The size, based on astronomical observations is 350 million light-years in diameter


The building block of the DSSU is the rhombic dodecahedron; the closest-packed polyhedron with 12 identical rhombus faces, 24 edges, and 14 nodes.

Each node is a center of gravity of a rich galaxy cluster

Credit: Conrad Ranzan


There is an observable presence of at least one super-giant elliptical galaxy at each node.

14 galaxy clusters are linked by 24 filamentous arms.

The arms represent the extensions of various galaxy clusters.

X-ray images of six galaxy clusters.  Credit: NASA/Chandra telescope


Cosmic cells are never isolated.  Nodes are always shared with neighboring cells.



Major and Minor Nodes – Rhombic Dodecahedron

Nodes absorb matter moving away from the voids and towards the filaments and clusters and aggregate the material.

Credit: Conrad Ranzan


Minor nodes

  • This is illustrated in the top circle above.
  • three filamentous arms meet
  • eight minor nodes
  • minor nodes absorb material from four filaments
  • corresponds to four-branch galaxy clusters


Major nodes

  • This is illustrated in the bottom circle above.
  • four filamentous arms meet
  • six major nodes
  • major nodes absorb material from eight filaments
  • corresponds to eight-branch galaxy clusters


This is the reason behind the variation in material aggregation and variation in observed richness of galaxy clusters.


There are more minor nodes than major – this accounts for the prevalence of moderate sized clusters and scarcity of major sized clusters.

Credit: Conrad Ranzan



Major and Minor Nodes – Rhombic-trapezoid dodecahedron


  • two minor nodes may be directly linked
  • two major nodes may be directly linked
  • 12 out of 14 nodes are paired this way



Rhombic vs. Trapezoid

When the cosmic cell is a rhombic structure galaxy clusters are equally spaced.

When it is trapezoid, the distance between nearest node clusters may vary by a factor of two.

Two closely spaced nodes can appear as one extra-large galaxy cluster.



Extraordinary Over-density in Galaxy Distribution

There can be flaws in the regularity of cosmic cells due to the intense variety of forces that occur in outer space upon galaxies.

Such flaws are known to occur in the surface patterns of thermal convection cells in liquids during carefully controlled lab experiments.

One flaw is cellular collapse.


Cellular Collapse

A cell can collapse to a point and become a single node.

In this case, six nodes have become one.

Credit: Conrad Ranzan


This results in an anomalously large concentration of links.

All membrane material becomes concentrated at one Supernode.




Supernodes have up to 32 links.

  • 8 minor nodes with 1 external link
  • 6 major nodes with 4 external links


The Great Attractor – ACO 3627 – is a possible example.



Galactic Clustering


Explaining Right-Angled Walls of Galaxies

As seen throughout the universe, galaxy sheets (wall of galaxies) are rather common.

There is always a rich cluster at the wall’s center.

Examples include: Cetus Wall; Sculptor Wall; Centaurus Wall; Great Wall (Coma cluster).

The Great Wall includes clusters Hercules, Coma and Leo on the right of this view of the local universe.


Some of the Great Walls meet at right angles!

See Cosmic-Scale Structural Features Explained by Conrad Ranzan.8

It is all about tilting and rotating these 3D structures to view them from different angles.

We will see below how this occurs.



Rhombic Dodecahedron

In a rhombic dodecahedron planes of all sides meet at right angles.

A hypothetical slice through a pair of dodecahedral cosmic bubbles reveals the main features of galaxy distribution:  rich clusters, voids, walls of galaxies and right-angled walls.

Tilt the structure forward and look down on a major node then rotate 45 degrees:  you can see the rhombic faces meet at right angles.

Credit: Conrad Ranzan


As seen below, a cross-section of the rhombic dodecahedron would be a hexagon.



Rhombic-Trapezoid Dodecahedron

The rhombic-trapezoid dodecahedron also has faces that meet at right angles.

Rotate the structure and tilt to look down on a major node at the center:  you can see right angles.

It also shows a semi-pentagonal shape!

Credit: Conrad Ranzan



In this article we have seen the geometric shape of galactic clusters according to Conrad Ranzan’s Dynamic Steady-state Universe Model.

It is to be noted that the large-scale structure of the universe is a commonly-accepted fact in astronomy.  The contention lies in admitting that this large-scale structure is based upon the Platonic solids, their compounds and duals (and how this could be), although the evidence is all around us.


In the next article we will go a bit deeper into Conrad Ranzan’s cellular universe to see that rhombic dodecahedral cells create gravitational cells that are tetrahedral and octahedral.  We will also discuss other scientists who have discovered the large-scale structure and noted that it was geometric in nature, particularly octahedral.


It is also to be noted that the existence of large-scale structure in the universe is only one of many examples of how the Big Bang (BB) Expanding Universe theory is incorrect.  If there was a Big Bang, then it would be expected for the materials in the universe to be randomly and somewhat evenly spaced.  At the very least, there should not be the same geometric patterns in the distribution of material in the universe if the BB theory was true.  It has been discovered that there is a large-scale structure and it is indeed geometric.  This alone blows the Big Bang theory out of the water.  It’s time to let it go and allow science to evolve, as it naturally should.


  2. Ranzan, Conrad, Large-Scale Structure of the Dynamic Steady State Universe. American Journal of Astronomy and Astrophysics. 4, No. 6, 2016, pp. 65-77. doi: 10.11648/j.ajaa.20160406.11
  3. Ranzan, Conrad “DSSU Validated by Redshift Theory and Structural Evidence,” Physics Essays, Vol. 28, No. 4, pp 455-473 (2015 Dec) (Doi: (Posted at:
  4. Gregory, S.A. and Thompson L.A., The Universe of Galaxies, Readings from Scientific American, Paul W. Hodge, editor, W. H. Freeman and Co., 1984
  5. Ranzan, Conrad, Large-Scale Structure of the Dynamic Steady State Universe. American Journal of Astronomy and Astrophysics. 4, No. 6, 2016, pp. 65-77. doi: 10.11648/j.ajaa.20160406.11
  6. Villanueva, John Carl, Structure of the Universe, 15 August 2009,
  7. Hadhazy, Adam, Why Nothing Really Matters: Gaping cosmic voids might hold the answers to dark matter, dark energy and the very foundations of the universe, 4 November 2016, Discover Magazine,

  8. Ranzan, Conrad, Cosmic-Scale Structural Features Explained, 2007,


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