Tetrahedrons: Rethinking Solids

Today, I was working on my business plan when I saw a pattern in the document.

Tetrahedron

I thought of minimal structures composed of tetrahedrons.

  1. A tetrahedron is composed of 1 tetrahedrons
  2. A octahedron is composed of 2 tetrahedrons
  3. An icosahedron is composed of 4 tetrahedrons
  4. A buckminster fullerine is composed of 20 tetrahedrons

It won’t make sense at first but think about the minimum number of tetrahedrons to account for all the vertices of a solid with one vertice ot the tetron at the center of gravity.

The Brain: ZenUniverse 4.0

zencircle011

“Tao can Tao not Tao”

Lao Tzu

I have been looking at the Platonic Solids and thinking about how they correlate to the five senses. I thought about the left and right hemispheres of the brain and realized that each of the Platonic Solids should be truncated to represent the right hemisphere. Now I had ten solids to work with. I worked backward from this and recognized I had to create a separate left right pairing of each of the senses to represent the brain correctly five on the left and five on the right. I have to create pairs of senses, trios of senses, quartets of senses and a quintet of senses. This is because these are ways we learn. We learn most when our senses are learning as a quintet.  This is why complete immersion in the environment we are to learn about is so effective.

This is a major revision of all my previous work.  However, I feel it provides a much more robust sensory model.

isaacnewton-1689

“To every action there is an equal and opposite reaction.”

Isaac Newton

Isaac Newton’s legendary statement was the premise of my new design.  I saw there were five Platonic Solids and as a reaction they would produce the five Truncated Platonic Solids.  This would influence all the components of the Solids.

Radeo

Dadeo

Radeons.  They are radical emissions.  These are based on the number of polytopes in the Platonic Solids.  These are your right  origins.

radeo2

Tradeo

Ideons.  They are Ideal emissions which are temporal radical emissions.  These are based on the number of polytopes in Truncated Platonic Solids.  This is your left percetual spatial origin.

ideo1

Audeo

Audeons.  They are audal patterns.  These are based on the shape of the faces of the Platonic Solids.  This is your right temporal plane.

audeo

Mudeo

Mudeons.  They are musical patterns which are temporal audal patterns.  These are based on the shape of the Truncated Platonic Solid truncation faces.  These are your left temporal planes.

mudeo1

Nadeo

Nadeons.  They are nasal intensities.  These are based on the angles of the Platonic Solids faces.  These are your right parietal arcs.

nadeo1

Gudeo

Gudions. They are gustal intensities which are temporal nasal intensities.  These are based on the angles of the Truncated Platonic Solid truncation faces.  These are your left parietal arcs.

gudeo2

Tadeo

Mates are Tadeons.  They tactal points.  These are the number of intersectin edges for each Platonic Solid’s polytope.

tadeo

Modeo

ReMates are Bodeons.  They are Basal points which are temporal tactal points.  These are the number of intersecting edges for each Truncated Platonic Solid’s polytopes.

modeo

Pyradeo

The pyramids contain the space of the radeons combined with the audeons.  Obtuse triangular pyramid, Right square pyramid, Right triangular pyramid, Right pentagonal pyramid, Acute triangular pyramid.

Ideo

Imadeons.  They are imadical solids.  These are a cound of the number of faces on the Regular Solids.

mageo

Video

Videons they are visical solids which are temporal imagical solids.  This is the the count of the number of truncation faces on the surface of the Truncated Platonic Solids.

video

Stateo Ateo Summary

brain

  1. GREEN: EYE: OCCIPITAL LOBE: visual center of the brain
  2. YELLOW: EAR: TEMPORAL LOBE: sensory center of hearing in the brain.
  3. SKY: NOSE: BRAINSTEM: control of reflexes and such essential internal mechanisms as respiration and heartbeat.
  4. BLUE: TONGUE: PARIETAL LOBE: Complex sensory information from the body is processed in the parietal lobe, which also controls the ability to understand language.
  5. ORANGE: BODY: CEREBELLUM: regulation and coordination of complex voluntary muscular movement as well as the maintenance of posture and balance.
  6. RED: MIND: FRONTAL LOBE: control of skilled motor activity, including speech, mood and the ability to think.

stadeo2

Link:

Systema: Geodesates, Nodes and Links

“To every action there is an equal and opposite reaction.” — Isaac Newton

A predominant issue arising from my work is the discovery of the difference between a node and a link.  A node type represents a state type while a link type represents a transaction between state types.  However I am finding there are a limited number of node types (self-ordered states) and link types (self-ordered state actions).

In the diagram below, each polyhedron is a first frequency geodesate and has a unique polytrope/polytype combination.  A polytrope is the number of edges per polyhedron vertex.  A polytype is the number of polyhedron vertexes.  This is not the final version.  I am still working to purify my geodesate concept.

What I am revealing here is that each of the seven Node Types on the Left has only one Link Type on the right.  In the same way that an association is composed of a source node type and target node type, an association is composed of a source link type and target link type.

Here is an example of a homogenous Entity to Entity association:

Here is an example of a hetergeneous Entity to Positity association:

Having considered this it is now possible to conclude that there are a unique set of nodes each with a unique link which can be used to build homogeneous or heterogeneous associations.  In otherwords, each node type can perform only one action type.  It is the reaction type of the target node type that makes the action reaction combination unique in the system.

Let’s look at some examples of node type and link type associations:

  1. To identify a positity, positifies an identity.
  2. To objectify a projectity, projectifies an objectity.
  3. To chronify a chronity, chronifies a chronity.
  4. To projectify a quantity, quantifies the projectity.
  5. To qualify an identity, identifies a quality.

Fourty-nine possible type combinations exist.  I think there are even more types which I will explore with Archimedean Solids and higher frequency Geodesates in later posts.

Systema: Geodesates as Singularities

“No one untrained in geometry may enter my house” — Plato

Over the past year I have been working with associative and relational databases attempting to find out more about how to develop a better database architecture.  This has taken me into many realms including network theory, chaos theory, state transition theory, geometry, logic, chemistry, biochemistry and physics.  Recently, I began to put these things together and I think I have had a valuable insight.  I call this insight “Geodesate Singularities”.

Geodesate Singularities regard networks as transitions between geodesates which are a group of convex polyhedrons.  Convex polyhedron networks have vertexes as nodes and edges as links.

What is of primary importance to this concept is the vertex enumeration (number of vertexes) and the polytope (number of edges per vertice) in these convex polyhedrons as geodesates are regarded as the most stable states.

First frequency Geodesates are a subset of the Platonic Solids and the Archimedean Solids:

  1. 3 edges per 4 vertices – 6 edges  – Tetrahedron
  2. 4 edges per 6 vertices – 12 edges  – Octahedron
  3. 3 edges per 12 vertices – 18 edges – Truncated Tetrahedron
  4. 5 edges per 12 vertices  – 30 edges – Icosahedron
  5. 3 edges per 20 vertices  – 30 edges – Dodecahedron
  6. 3 edges per 24 vertices – 36 edges – Truncated Cube
  7. 4 edges per 30 vertices – 60 edges – Icosadodecahedron
  8. 3 edges per 60 vertices – 90 edges – Truncated Icosahedron
  9. 3 edges per 60 vertices – 90 edges – Truncated Dodecahedron
  10. 5 edges per 60 vertices – 150 edges – Snub Dodecahedron
  11. 3 edges per 120 vertices – 180 edges – Great Rhombicosidodecahedron

Higher frequency Geodesates are triagulations of the above solids.  I recommend downloading the Mathematica Player and the Mathematica Demonstrations Project Geodesate Demonstration to view the polygons for each frequency.

Again, what is important in the Geodesates are the number of vertexes (nodes) and edges (links).

My hypothesis is when the growth of a network achieves the vertex enumeration and polytope of a geodesate at the first frequency or higher, a singularity state exists in the network order and results in a state transition of the network when exceeded.

Increasing a Geodesate’s frequency involves dividing the faces of the chosen polygon into sub-triangles:

The first frequecy subdivision is termed as 1V, second as 2V, third as 3V and fourth as 4V.

1V Icosahedron Geodesate

12 Vertexes – 12 5 Edge Polytopes

2V Icosahedron Geodesate

42 Vertexes – 12 5 Edge Polytopes – 30 6 Edge Polytopes

3V Icosahedron Geodesate

92 Vertexes – 12 5 Edge Polytopes – 80 6 Edge Polytopes

4V Icosahedron Geodesate

162 Vertexes – 12 5 Edge Polytopes – 150 6 Edge Polytopes

I think geodesate singularites have  implications for Telic, Organic, Chemic, Physic, Static and Gegonic networks.  This has implications for Ray Kurzweil’s Singularities, Malcolm Gladwell’s Tipping Points, Stuart Kauffman’s Self-Organization and Howard Rheingold’s Cooperation Theory.

Convex polyhedrons and geodesates could create and limit new organizational structures for enterprise goals, personnel, products, measures, spaces and schedules.

Related Links:

Icons: The Czerepak Framework

Beyond the Singularity

Physics: Observer as a State

Sociology: The Six Adopter Types

Icons: The Czerepak Framework

Tearing apart the Zachman Framework has yielded great results.  I have identified the core nodes and links (we won’t use the terms entities and associations any more).  The new Nodes of the Czerepak Framework are:

  1. Computers
  2. Machines
  3. Goals
  4. Observers
  5. Elements
  6. Particles
  7. Points
  8. Events

The new Links are:

  1. Operations
  2. Processes
  3. Rules
  4. Names
  5. Bonds
  6. Quanta
  7. Distances
  8. Durations

If you look at the link icons you can see what I am hypothesizing as the optimum cardinality for each.  I am thinking about this from the perspective of the Platonic solids, R. Buckminster Fuller’s work, Stuart Koffman’s work with chaos theory and Boolean networks and Albert Einstein’s own love for geometry.

The set of icons created to this point are below: