EM education | Zome geometric modeling

What is Electromagnetic Education?

– Zome geometric modeling –

GENERAL purpose modeling tools have a wide-range of applications when studying electromagnetism. Zome is one such tool. It enables visualization of electromagnetic concepts which range from models of atoms and molecules to electric transmission powerlines, limited only by imagination.

AS a versatile modeling tool Zome enables mathematic modeling at the same time as offering a unique structural platform that could be an effective means for light-weight frames for do-it-yourself robotics. (Visit the manufacturer's website to learn more about the 61-zone Zome System, its mathematical basis, and relation to the Golden Section, Fibonnacci Sequence, and 2-fold, 3-fold, and 5-fold symmetry.)

THIS 'ball and strut' geometric system offers a way to design and build small-scale spatial structures which are not limited by the complexity of square roots and diagonals of various lengths and angles. This quality enables complex geometries to be constructed quickly and with ease and understanding.

FOR example, a 'tetrahedron' is a Platonic solid whose pyramid shape was believed to represent fire. The balls and struts which compose a tetrahedron relate to those structural connections which make up the material world of matter, held together by clouds of electrons sharing interatomic orbits.

Tetrahedron modeled using Zometools.
©-free, photography by electronetwork.org, 2004.

PHOTOGRAPHING the Zome tetrahedron and importing it into graphics software, one can add additional visual information such as 'electron clouds'. If these were to represent the chemical bonding of atoms, each strut would be a bond, and each ball an atom. In this case the tetrahedron has the same atoms at the 4 points of its vertices, the geometry of which also indicates how the molecule is packed. In this case the tetrahedral electronic structure consists of four phosphorus atoms with six interatomic bonds, also known as P₄.

Zome Tetrahedron with electron clouds added by software.
©-free, photography by electronetwork.org, 2004.

UPON experimenting with Zome modeling, the memory of a book encountered years ago in a used bookstore came to mind. The Architecture of Molecules by Linus Pauling had beautiful pastel drawings of molecular structures by Roger Hayward. It was checked out of the local library and became a way to learn about and study the electronic structures of molecules and atoms as a result. Apparently this connection was not unique: the idea for Zome was inspired by this same book and its illustrations, and Linus Pauling has even used the Zome modeling system.

The Architecture of Molecules - Pauling and Hayward

The Architecture of Molecules. Linus Pauling and Roger Hayward.
W.H. Freedman and Co., San Francisco, ©1964. LoC #64-7755.
Educational fair-use of copyright, electronetwork.org, 2004.

ESSENTIAL as a companion text to using and exploring Zome, The Architecture of Molecules offers a concise and beautiful view into the harmony between pure mathematics and molecular geometries which at times nearly mirror these, give and take the forces between atoms and the variable angles of atomic bonds. It is remarkable to witness the correlation between Platonic solids and the moving electronic clouds of chemistry, and how any slight variation changes the composition of matter itself.

The Architecture of Molecules geometric electronic structures

The Architecture of Molecules, pastel scientific illustrations
by Roger Hayward of the geometries of electronic structures.
Left: Icosahedron (32). Right: Decaborane Molecule (35).
Educational fair-use, electronetwork.org, 2004.

ONE such example is found between the Icosahedron whose form was associated by Plato with water. Its 20 triangular faces, 30 'strut' edges, and 12 vertices are found partly constituted in the Decaborane Molecule, as noted by Linus Pauling. Ten boron atoms reside at the vertices of the icosahedron, which are bonded to hydrogen atoms off this molecular structure of B₁₀H₁₄.

LIKEWISE these same chemical structures can be approximated using Zome modeling to visualize the electronic composition of the material world. Critical to this approach is to simultaneously show the geometrical context for a given molecule.

METHANE demonstrates the value of this approach. The molecule inhabits a tetrahedron (defined by white struts) while the atoms are modeled using other colors. The carbon atom (black ball) has interatomic electron orbitals (yellow struts) with the four hydrogen atoms (yellow balls) found at the vertices of the tetrahedron.

Zome modeled methane molecule with software electron clouds

Methane molecule model with software electron clouds,
nested inside the geometric structure of a white tetrahedron.
(black zome ball = carbon, yellow zome balls = hydrogen,
yellow struts = shared electronic structure of atomic orbits).
(CH₄) ©-free, photography by electronetwork.org, 2004.

AFTER photographing this model, the image can be brought into graphic software to add additional details, such as the electronic clouds around the atoms, in this case using a distortion filter to visualize, dynamize, and conceptualize CH₄.

OF particular interest in the connections found between electronic matter and pure geometries is the boundary where great mysteries still reside. Of the five Platonic solids, one stands out: the tetrahedron relates to fire, the cube to earth, the octahedron to air, and the icosahedron to water. Yet there is a fifth element, the dodecahedron, that is a significant cosmological pivot in electromagnetic understanding (Michelson-Morley) and remains a conceptual enigma to this day: the aether.

Zome model of the aether, the 5th element

MODELING the aether as a geometric shape is another aspect of using Zome models for conceptual exploration of ideas, as it functions as a symbol in this case. All the questions of dark matter, dark energy, new energy, and other forces may someday relate back to ideas carried within the puzzle of the 'immaterial' aether and its material relation to the rest of the universe of matter, geometry, and unifying perspective. In other words, the idea of the aether may function as a type of 'unknown' which keeps electromagnetic questioning open to new discoveries, ideas, inventions, and also keeps minds open to possibilities.

SYMBOLIC models offer another option for representing ideas. For instance, architectural and engineering structures such as trusses with metal frames are easy to imagine and quickly build using this system. The models can then be photographed and manipulated using software to add additional details. One could mock-up the design of a building or even infrastructures, and present the new ideas through proposals.

Zome electrical transmission pylons in Japanese garden

Zome models of electrical transmission pylons in Japanese garden.
(click to enlarge) ©-free, photograph by electronetwork.org, 2004.

POWERLINES and subsequent power transmission pylons and other wooden and metal infrastructures are areas where design innovations await, and which Zome modeling allows easy access to new ideas and alternative experiences. Landscape architecture offers many examples throughout history of the juxtaposing of ideas in the natural and built environment. Mediations such as those designed by Christo have parallels in geometric relationships between structures and forms, as with Plato's solids and The Architecture of Molecules as described by Linus Pauling.

JUXTAPOSING of pure geometric forms in an organic Japanese rock garden is one way of experimenting at a smaller scale, yet which puts these views into sharp relief: what if all the transmission towers that occupy the land were more harmonious with their setting, with structures that gracefully touched the ground and also brought a new sense to the experience of the total environment - including the symbolic four elements of air, fire, earth, and water, in addition to the fifth element of the aether. These traditional infrastructural design elements could be reinterpreted anew by modeling these new views of everyday environments.

Zome model of a 'BuckyBall' or Carbon 60 molecule, named after
R. Buckminster Fuller. Could it be a future electrical substation?
©-free, photograph by electronetwork.org, 2004.

GEOMETRIC modeling offers diverse options and innovative approaches to learning more about electronics and electromagnetism limited only by the imagination. A few approaches to learning more about atoms and molecules have been demonstrated in addition to aiding in conceptualization and the modeling of new ideas for infrastructures, to share electromagnetic ideas, inventions, and knowledge through the process of building them. (bc 12.20.2004)

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