Progress

Yes,...really....things are beginning to move forward with the hexaflex matrix/latticework.
An educational toy is the most advantageous application of Hexaflex.
Educational in the sense that for both children and adults it teaches a new spatial awareness based on the 120 degree geometry of the hexagon and the rhombic dodecahedron rather than the 90 degree geometry of the square and the cube.
Further, It would appear that this "toy", or what would be better described as  a "scientific three-dimensional modelling kit"  holds a few secrets.

After having the prototypes 3-dimensionally printed, I, at last, had in my hands the very essence of the geometry of all of the forms (Allotropes) that carbon can take. Diamond, graphite, graphene, Fullerenes, Buckyballs, Lonsdaleite, Nanotubes. With this modelling kit  I’m viewing it more as a better carbon molecular modeling kit.
Within the Hexaflex lattice, the hexagonal tile represents the carbon atom whilst the rectangular tiles represent the bonds between adjacent carbon atoms known as the Van de Waals forces of attraction. These forces bond the sheets of graphene together to make graphite.
The problem with the present ball and stick molecular modeling kit is that molecular systems with arbitrary angles cannot be built. In contrast this new form of modelling system is dynamic with complete freedom of movement. As a toy it provides a new experience in tactile handling. 

Why Hexaflex?

Yishu Dai 
I still don't' get the concept of hexaflex though, why are we trying to find them, and what's special about them that we're trying to find them?
January 1 at 11:26pm · Like

Bob Burdon 
Welcome to all of my newly acquainted friends and visitors. 
Thank you all so much for joining this group of "Think Tankers" . De Bono would be proud!

Our Quest is to find this honeycomb lattice which I call HEXAFLEX.

This design is elegant and simple in its construction.
Yet for all of its geometrical simplicity it had never been discovered until I serendipitously found it 5 years ago. 

That fact alone is staggering

In that time, with the help of my good friends David, Janice, Kelvin and Seth, a patent was granted in June 2009.

We have identified many possible applications for Hexaflex but there is one thing which continues to elude us.

WHERE DOES MOTHER NATURE USE IT ????????????

For all our skill and technological prowess, human engineers still can't match Mother Nature's best designs. Her designs are always simple elegant and efficient.

In order to help us focus on this quest I am gathering a collection of images of all natural things which have a degree or two of hexagonality about them.
By carefully analysing these images we may gain a clue.

I believe that this geometrical discovery has great significance in science. It could be the precept to precipitate a concept to finally precipitate a paradigm. 

This quest will open a door into another world of possibilities.
We may find its existence in the human body. 
Perhaps it exists in the nanoworld .
Perhaps its the Herpes virus capsid.

Perhaps in your own field of interest/profession you may recognize where Mother Nature is could be using using the Hexaflex latticework.

Perhaps we could grow T cells on it.

Perhaps a true mechanical skin.

Perhaps..............Fill in the blank.

Time to flex brain muscles!

Feel free to explore all aspects of this site.

Scroll down to 'Photos' and click on 'See All'.

If you are enthused by any particular photo in the album and have a comment that you would like to leave then please feel welcome.

Positive, negative, leave a link, leave a video, upload photos.

Our think tank will surely reach a critical mass of thoughtful input. 

Feel free to invite your friends to our group. 

Aloha,

January 1 at 11:30pm · Like

Yishu Dai 
thank you i did read this, but i'm so confused about how exactly this design is helpful
January 1 at 11:44pm · Like

Bob Burdon 
To find this exact latticework in natural engineering has been the aim of this quest. 
It has unique properties. 
This latticework is governed by a simple geometrical pattern of rectangles with hexagons. The pattern of the layout evolves from the three dimensional geometric tessalation of rhombic dodecahedrons. This pattern is the only one, of many, which allows this two-dimensional pattern to be folded, concertina style, into the third dimension. 
It is based on pure geometry. 
With that in mind, it became my belief that this latticework had to exist somewhere in Mother Nature's toolbox. 
To date, with a limited number of 3D printed prototypes (try saying that fast!) It can model all the allotropes of carbon. As a molecular modelling kit it has the potential for furthering both research and discovery in nanotechnology where I believe it was hiding all along. 
Bio-mimicry.
It mimics the surface of a scale on a butterfly wing. That could be a line of good enquiry and research.
This design makes an amazing toy for both kids and adults.

Hexaflex the Quest

Exciting things are beginning to manifest.
I have been trying, for the last seven years, to find where this simple "Hexaflex" lattice could be found in Nature.

I have found similarities to it in Sodalite, butterfly wing scales and capsid geometry.

My very recent research has led me to graphite which appears to be an exact fit. I have been unable to find any information which points to the knowledge of this discovery. It still appears to be unknown to Acedamia. I am keen to get a second opinion.

Photographs and background can be found at Hexaflex the Quest on Facebook. Please visit and consider joining this quest.

Hexaflex the Quest.

Graphite Side A

Hexaflex SideA

Graphite Side B

Hexaflex Side B

Hexaflex Nodlet

Graphene

The Hawaiian Green Turtle

These unique hand made sculptures are derived from a geometry between the hexagon and the square to create the shell of the Hawaiian Green Turtle. Serendipitously, the resulting geometry has the perfect openings for the wooden head and limbs to be placed. Only local Hawaiian woods such as koa, mango, milo, mac-nut and lychee are used.

The Hawaiian green turtle is an important symbol in the mythology of Hawaiian culture.

The Honu is a Hawaiian symbol of creation, longevity, peace and the spirit within.

In Chinese mythology, the sea turtle also represents wisdom. The shell of the turtle is said to have the markings of heaven and earth upon it. It is also said that the Turtle had risen from the depths with the markings of the eight trigrams on its back. These are used in the I Ching and the Bagwa.

☰☱☲☳☴☵☶☷

The sea turtle mirrors the health of our planet and the struggle for survival for these ancient creatures is in our own hands.

"Nanosphere"

Yang Nanosphere

Ying Nanosphere

“The Nanosphere.”Sculptured by R.L.J.Burdon.

My current body of work focuses on hexagonality.

This is one of many spatial studies to be undertaken.

The inspiration behind my artwork is a unique set of three matrices that I serendipitously discovered. 
By following natural forms of geometric symmetry and proportion, I try to manifest geometric flowing architectures that reflect the elegance of our beautiful macro/micro world.

Crafted from copper sheet entirely by hand, this totally unique design is based on a geometric relationship between the hexagon and the square to create this double layered sphere.

The metaphysical properties of Copper.

Copper has the power to heal the mind and body based on the metal’s energy conducting properties. Copper can stimulate the flow of energy and hence move psychic or mental energies thereby helping the immediate environment to overcome lethargic tendencies, resulting in more vitalized and amplified thought processing. This energy vibration of copper is well known for its healing and transforming properties.

This newly discovered geometry connects both the inner and outer spheres together creating a subtle potential energy matrix.

The matrix having two different surface architectures allow either a Yin or a Yang type surface.

The geometry of the matrix allow the sphere to expand by approximately 15% in diameter.
more pictures

Workshop

Tools Required.

Swivel head shears, Drill, Files, Hammers, Clamps, Propane torch.

• Materials.

24 gauge copper sheet, solder, flux, wire wool, contact adhesive, acetone.

• Cutting.

Cut out 1 blank approx 10” x 12” from copper sheet.

• Drilling.

Sandwich the copper blank between the 2 pieces of the drill guiding jig. Drill out 78 qty 1/8” holes. The jig places these holes 1” apart. The overall pattern delineates a snowflake design.

• Chiseling.
Using a 1” width chisel the snowflake pattern is cut out from the blank.

• Cleaning.

The pattern must be cleansed of all greases and oils in acetone prior to the gluing and forming process .

• Gluing.

Hexagonal cross sectioned forming dies are glued using contact adhesive to both sides of the pattern.

Forming.

Using hand applied pressure and manipulation the pattern is concertina folded in upon the forming dies.

• Cleaning.

The Forming Dies must be removed by a prolonged soak in thinners.
Contact adhesive and residues are also removed in prep for soldering.
Surfaces to be tinned are cleaned with wire wool prior to fluxing.

• Fabrication

These patterns are now tinned and soldered to each other to form a sphere

• Fettling.

The sphere is cleaned of excess solder and all edges are fettled and smoothed

• Patina.

The sculpture can be given a variety of different patinas ranging from iridescent blue to shimmering green using different chemical washes and varying heat treatments.

Posted by Bob Burdon at 5:38 AM

The Satkona Yantra

A new and yet again innovative matrix design utilizing triangles and squares allows the sculptor to create a mandala symbol called satkona yantra or sadkona yantra found on ancient South Indian Hindu temples built thousands of years ago. It symbolizes the Nara-Narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in "Moksha," or "Nirvana" (release from the bounds of the earthly world and its material trappings).
A Yantra is meditational device used in Hindu and Tibetan Tantric meditation.
From the root "yam," meaning "to sustain," the Yantra is a symbolic image used to maintain a focused state during meditation. A Yantra is usually composed of an outer geometrical form enclosing an interior geometrical design. Each particular design is used for a specific purpose or intent.
Some of the basic elements of a Yantra are:
Ø The Bindu, or infinite point.
Ø Upward and downward facing triangles, symbolizing a female, watery energy, and male, fiery cosmic energy.
Ø A hexagram or six pointed star (satkona), symbolizing the union of Shiva and Shakti, masculine and feminine energy.