Thursday, 17 January 2019



The FFELLONIC FORMS are a new fundamental series of geometrical forms. They are created by connecting lines between the centres of naturally attaching spheres which form a finite series of twelve arrangements. 

Introduction The five regular, convex polyhedra called the Platonic Solids have captivated the interest of many famous scholars over the centuries.

Plato, Kepler and many others have tried to understand the Platonic Solids and ultimately discover a link with Nature. This has lead to their characteristics being aligned with planets, elements and any natural pentagonal occurrence. 

There has been many books written outlining the Platonic Solids's unique characteristics, with many explaining their perceived philosophy and meaning. However, it is very hard to find any explanation for them other than discussing their physical properties or symbolism.

On Googling “Platonic Solids” there is plenty of information on how they are defined, how to make paper models of them and the clever ones will even give you their proof why there are only five. But even with this great resource there is very little written which explains them.

So even with all of the available knowledge when you start to study these structures further, which everyone confirms are so special, there is virtually no information that helps you to completely understand the Platonic Solids and discover their simple link with Nature which is the goal of everyone.

However things are different with a new series of geometrical structures called the FFELLONIC FORMS as the whole story can now be completed and it allows for a greater understanding and confirms the potential of the Platonic Solids.


To explain the complexities of Nature a four dimensional dynamic model must required. 

Unfortunately, the Platonic Solids are viewed as three dimensional solids and will fundamentally never achieve any link with Nature if they are described this way.

The problem is that the Platonic Solids are always defined by a traditional definition based on the observation or description of a solid:

"regular, convex polyhedra with similar, regular polygonal faces that have the same number of faces meeting at each vertex".

Following the application of all these parameters, the degree of freedom to realize their full potential is limited.

 By following this definition only five polyhedral shapes will ever be formed.

So not only is the definition of the Platonic Solids limited to polyhedra but also shape, without any consideration of their relative size. When size is taken into consideration we find there are six Platonic Solids.

As a result of not being able to understand them they have been regarded as a mathematical curiosity and other than making models of them have been of litle interest to academics.

However, the ancients were right when they said there was a link between the Platonic Solids and Nature, however it is not found by observing their physical characteristics but the dynamic process involved in their construction. 

If past scholars had defined them by this way they also would have understood the Platonic Solids and realised they are part of the larger series of twelve geometric structures called the FFELLONIC FORMS. 

A fundamental aspect of the Platonic Solids is that they have no substance and they are definitely not solids, being created  by connecting lines between the centres of naturally attaching spheres.

The geometry of the Platonic Solids is based on the following arrangements of naturally attaching spheres.

by connecting lines between the centres of the naturally attaching spheres 

             Tetrahedron                                     Octahedron                                            Icosahedron      

or using the central point of the spheres as the face as in the following                                                                                     
              Inverted Tetrahedron                     Cube                                           Dodecahedron

Bringing the two together

The preferred group is the first one which uses the centre of each sphere for its vertices, as it helps to better identify the spheres and their arrangements. 

The spheres and how they naturally come together is the defining feature of the Platonic Solids not their final shape. The lines connecting the centres of the spheres creates the geometry of the Platonic Solids which is only a map or chart of these arrangements and therefore has no substance. 

When similar spheres initially attach to each other they will form the following initial designs These will gradually grow as further spheres with the same capacity to attach come together.

As more spheres attach the distinctive arrangements of Platonic Solids arise.

As the spheres on which the Platonic Solids are based come together the following happens:
  • the adjacent spheres are arranged symmetrically around a central axis 
  • the axis is directed to a centre of the initial form being created. 
  • each arrangement is identical and constant in design throughout the final structure

The big question to ask  is why no one had ever bothered to expand this series by using the same natural principles by which the Platonic Solids are formed. By increasing the same number of spheres attaching at each vertex.

When the above criteria of the base units of the Platonic Solids of the primary group are fully applied the result series is not three structures (Numbers 3, 4 and 5) but twelve FFELLONIC configurations of spheres at each vertex.

The arrangements grow as similar spheres combine to automatically form their respective final structure.

As similar base units come together at the different Levels they naturally combine in turn to form the twelve individual FFELLONIC FORMS of which the primary group of Platonic Solids are only a part.


Level One  -  Single Line 

A single line which is the First Level of the FFELLONIC FORMS is formed when the centres of the two spheres are joined.

Level Two  -  Triangle

When the centres of three spheres are joined by lines a triangular form is the result.               

Level Three  -  Tetrahedron   


Level Four  -  Octahedron


Level Five  - Icosahedron


  An Icosahedron is not a solid as there is no sphere in the centre. It is a shell about to open out with a further degree of freedom in to the triangular tessellation of Level Six.


The following are the first five FFELLONIC FORMS which includes the Platonic Solids. As more come together there has to be more organization to maintain the symmetry.

Level Six  -  Triangular Tesselation
The completion of the first half the FFELLONIC FORMS with the spheres coming together on one plane to form an extensive triangular tesselation.

Level Seven  -  Linear Truss


Level Eight  -  Pyramidic Spaceframe


Level Nine  -  Tetrahedral-Octahedral Spaceframe

Level Ten  -  Truncated-Octahedral Honeycomb (Final Outline)

11. Cub-Octahedral Honeycomb (Final Outline)

12. Tetrahedral-Octahedral Honeycomb

It is that simple. By applying the same rules by which the primary group of the Platonic Solids are constructed, the final result is twelve dynamically formed and individual structures called the FFELLONIC FORMS. Remembering that they are not solids but a map or chart of naturally attaching spheres.

There is now a great opportunity to have a deeper understanding of the Platonic Solids and properly investigate further the link with Nature which Plato and others sought.


The FFELLONIC FORMS are an amazing discovery and the inferences that can be made from their construction will lead to many more.

Any feedback would therefore be gratefully received. Tell me if it is not correct or the wrong assumptions are being made or it is not relevant. I will do my best to respond, after all if the FFELLONIC FORMS are that good I should have all the answers.

Twitter  @ffellonicforms

Copyright © 2015, 2017  David Fell. All rights reserved.

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