Sunday, October 7, 2012

Sacred Geometry, Chirality and the Cyclohedra

Tetracyclohedron on a mirror - cast figure - DS 1988

"We live on a planet which is essentially a rotating sphere, in a system comprised of other rotating spheres. These revolve around a rotating ball of burning gases in orbits that roughly describe a series of concentric rings. This system, in turn, is rotating within a spiral galaxy, which, in itself is also rotating with a host of other spiral and spherical galaxies in what some hypothosize to be a circular universe. In view of this, how else can the "phenomena of life" behave? How could it possibly extricate itself from the "spiral urge"? Worlds turn, cells divide, and flowers bloom using rhythmic processes not wholly deciphered by mechanistic equations. Physical laws and physical life must, by necessity, share a common ground, and this "ground", this mysterious omphalos, appears to be round."


"In the end one cannot help but sympathize with old Archimedes who, while drawing circles in the sand, allegedly remarked to a passing Roman soldier - and, presumably these were his Famous Last Words - 'Don't step on my circles!'"

- two excerpts from the intro to Cyclosymmetrics, The Implicate Geometry of the Circle - 1993, Dia Sobin


Geometry confounds, but it never lies. And, when the going gets tough, the tough draw circles. Which is why I'm posting geometry today, despite its obvious departure from recent material.

Above is what almost seems like a Brancusian structure. What it really is, however, is a photograph of my first casting of a cyclohedron - specifically, a tetrahedron -  sitting on a mirror.  As for Constantine Brancusi, I discovered today he was Romanian, born in a similar place in the vicinity of the Carpathian mountains as both sets of my grandparents. He was a very spiritual man, and I find it interesting that geometry and the spiritual seem to intertwine in so many respects. Geometry is so subliminally present in so many aspects of life, it's not unusual that it was always, an still is, a "sacred" discipline. 

Re: cyclohedron. You won't find the word in Wiki, or anywhere else for that matter (but here, presently)*, because it's one I coined to describe a set - specifically, the Platonic cyclodhedra - which describe a regularly convoluted set of polyhedra - I inadvertently discovered in the 1980's during the course of a design project. I've tried to document them myself - the quotes above come from its introduction - but, as I have had no intensive mathematical training, I never attempted to publish my "treatise". I did have a web-site several years ago - "The Circle Zone"  (I've just up-loaded its home page graphic here...) -  but apart from one Chinese teacher (and new media artist) Zhang Yanxiang - and Petral, if you're out there, I am eternally grateful - it didn't attract a great deal of attention. Why those from the East might find the cyclohedra attractive, is not unusual. The figures emerge from the circle and its infinite symmetries, and the East has an intimate relationship with the circle, in ways the cruciform-fixated West could never quite comprehend. (see Mandala)

Page 65 from Contemporary Art of Science and Technology - Science Press - 2007
Funded by: China Association for Science and Technology, and the
National Philosophy & Social Innovation Base for Sci-Tech History & Sci-Tech Civilization

Specifically the figures literally enfold from an expansion of an ancient pattern called the "Flower of Life", or, as sacred geometer, Charles Gilchrist, refers to it: "Natures First Pattern."  There a number of correlations that are drawn - either metaphorically or demonstrably -  to this pattern and the natural world... but, allow me to add another one: quantum entanglement

Chirality, on the other hand, is a word most often used in physics and chemistry to describe symmetries that are applicable to those disciplines. But, chirality also describes what differentiates the cyclohedra from their rectilinear counterparts - the regular polyhedra - in that, two orientations of the planes are possible... a left-handed twist, and a right-handed one. The two "pinwheels" I created from the tetrahedron photo, for instance, are "spinning" in opposite directions. They're admittedly odd formations...almost alien really... and I often muse about an intelligent alien race - or perhaps just a parallel one - which developed along the devious, organic lines of a cyclohedron as opposed to those static, antiseptic rectilinear planes of the regular polyhedra, or Platonic solids, we know so well.

Rotational symmetry - (top) 6-fold - (bottom) 8-fold - DS 2012

Fractals, of course, are a visual example of organic geometry... the cyclohedra are another. Demonstrably, the circle is the mother of all geometrical figures, organic or inorganic - the dynamic of the material world... and whether you are an artist or a scientist, your inquiries inevitably resolve themselves in her domain. My geometrical muse is adamant about this, and I trust this muse implicitly. As I said, geometry never lies.

A second set of Platonic Cyclohedra cast in 1993 - DS

Cast tetracyclohedron & octacyclohedron (using 120 degree arcs) on a mirror
1993, DS

Vesica Piscis

*  Recently (2/28/14) I found this entry for the word "cyclohedron" on Wolfram. I have no idea when it appeared, when the word was coined, or, in fact, what it's referring to... however, I am continuing to use the word regarding the solids depicted here.

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