Tagged: hexagons

A polyhex is a plane figure composed of n regular hexagons joined at their edges, in the manner of a regular hexagonal tessellation.

Polyhexes have perhaps achieved their greatest utility in organic chemistry, where they can be used to represent various configurations of aromatic hydrocarbons, but are also often employed in puzzles, logic games, and other recreational mathematical pursuits. A more speculative application of the first several orders of free polyhexes can be found in Patrick Mulcahy's article The Hexagonal Geometry of the Tree of Life, available as a PDF file in our Hexagonal Library.

Today would be a good day I think to take a break from not-updating this site to remind everyone that this year's Hexagon Project at Interdependence Day Scranton is currently underway. I hadn't been planning on writing another post about it this year, but of late I received this lovely promotional poster, which I thought at least worth relaying to the wider hexagonal community. In commemoration of this year's festivities, I have also added to the Hexagonal Library a PDF of a presentation by Hexagon Day organizer Beth Burkhauser to the National Art Education Conference, "Global Interdependence and Art Education: Where Hexagons Make the Connection." More musings on the project can also be found in last year's blog post on the subject. In general of course HEXNET.ORG supports all efforts to relate the civic virtues of hexagons to their more familiar geometric ones, as both are clearly manifestations of the same unified underlying reality.

Here we see an arrangement of hexagonal clouds photographed by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor aboard the Terra satellite on 6 June, 2002.

Here we see several illustrations of John Leighton's proposal to divide Greater London into a series of hexagonal boroughs, as described in his book The Unification of London: The Need and the Remedy.

I have recently been made aware of a contest being held on Kotaku Australia regarding "hexagons that should not be." Apparently inspired by the hex tiling in Civilization V, they are giving away a free copy of the same to whoever most impressively photoshops a hexagonal shape onto an object that is not normally hexagonal. Unfortunately, the contest ends Monday night, so there's very little time to spread word of this to the larger hexagonal community. I wish I'd heard about it sooner. Anyway, samples of submitted work can be found on the following pages, and are most interesting:

• Some Of Your Civilization V Competition Entries
• More Civ V Competition Entries
• Your Six-Sided Take On The World

[Edit: The winners and runners up can be found here and here, respectively.]

I find it fascinating, obviously, both as a Civ fan (still trying to get 5 running under Wine!) and as a hexagonalist. Creative exercises of this sort, inducing people to think artistically about the roles and potential roles of hexagons in everyday life, are potentially very valuable tools in expanding hexagonal consciousness. It reminds me in some ways of last month's Interdependence Day Hexagon Project—in both cases, the hexagon is explicitly employed not for some incidental aesthetic reasons, but for its very hexagonality itself. This can only be, I think, a positive trend in our society, as we as a species come to terms with the implications of our glorious hexagonal future. I am hoping to see more and more of this sort of thing in the coming years, as hexagons rise to ever greater prominence in the collective human experience, perhaps leading at some point to the formation of an explicitly "hexagonalist" movement in art and design.

Breaking news from the world of HEXAGONS:

While reviewing the hexagonal news this morn, I ran across an article describing some sort of Hexagon Project out of Scranton, Pennsylvania. Looking into it further, I expected to find that—like many hexagon-identified things these days—the "hexagon" was a purely metaphorical branding feature. To my surprise though, it not only involves literal hexagons, but the hexagonal geometry seems to have been deliberately and consciously chosen for very hexagonally-aware reasons. The project's page explains, under the heading "Why a hexagon?":

"The hexagon is a composition of complex relationships, interdependent lines, like bonds of human connection, strengthened in multiples into an infinite network of connections. It maintains its own presence as a shape, symbol of light and life, yet, structurally, destined to be part of a whole—a splendid architectural element, infinitely expandable."

[Edit 2013-10: The existence of this post has bothered me since I first published it three years ago. Basically, this was intended as the first installment of what was to have been a sprawling series of posts attempting to reconcile what I will loosely term "Eastern monism" with the semantically precise, mathematical ontology I have been trying to develop in light of hexagonal principles—and in a real, meaningful way, not just in some fake-ass pop quantum mysticism sense. I won't recapitulate my whole line of thought here, but suffice to say I had and continue to have more substantive and I think relevant ideas on these matters than those expounded in this limited post, which by itself I think ends up conveying either that I misunderstand or misinterpret people like Watts, or that I am not particularly interested in the finer implications of what they tried to communicate. And I would like to think neither is true. Watts was a huge intellectual influence on me in my youth, and it was writings such as his that actually turned me from my earlier phase of hexagonal thinking as a teenager—only to return to it with more clarity of thought over a decade later. And having later become of aware of his passing references to hexagons, I was very eager to draw out these ideas and sort of riff on them with the greater perspective gained from the ensuing years. But I left the task unfinished, and, again, I think this post, by itself, is sort of weird. I gave serious thought to deleting it or leaving it unpublished in this latest iteration of the site, but ultimately decided to leave it here, with this disclaimer. I intend to revisit these issues at some point, hopefully in greater detail, at which point I will perhaps modify or edit this post further.]

"Where is it writ large that talking monkeys should be able to model the cosmos?" – Terence McKenna

I remember reading a short but eloquent endorsement of hexagons by Alan Watts once, probably seven or eight years ago. Since I wasn't particularly interested in hexagons at the time, I quickly forgot about it, and where exactly I had read it. However, times have changed and my hexagonal thinking has evolved, and with the advent of Google Books and all, I recently decided to look into the matter further. After an exhaustive search, I found two mentions of hexagons in Watts' books, which I shall now share with you, and duly expound upon.

I am not entirely sure either of these is in fact the passage I remember reading, but if it were either of them it would be this first one, which can be found in the essay What on Earth Are We Doing?, from the collection Cloud-Hidden, Whereabouts Unknown:

Anyone following the hexagonal news of late has no doubt noticed a flurry of stories related to the upcoming release of Civilization V, and in particular its new hexagonal tile system. In this blog's opinion, the adoption of hexagonal tiles by the Civ franchise is a long overdue development, and frankly one that should've been incorporated into at least the last two Civ releases. Indeed, many DOS-based strategy games have used hexagonal tiles going back to the late '80s, and one has to wonder why Civilization ever used square tiles. (I remember playing the original Civilization in the early '90s, well before the advent of my own hexagonal illumination, and thinking that, in fact, it would be better with a hexagonal grid. I can only imagine part of the media excitement here—aside from just the general awesomeness of hexagons—is due to the fact that many, many other people have had the exact same thought over the past twenty years.)

Metatron is an angel described in Jewish and other Abrahamic religious texts, variously identified as the Scribe of God, the Lesser Tetragrammaton, et cetera. He/it is closely identified with the prophet Enoch, and by many accounts they are one and the same entity.

The cube itself consists of thirteen (doz. 11) circles, six of which emanate out from seven hexagonally packed circles in the center, with line segments connecting the center of each circle with the center of every other circle. This has the effect of producing a highly hexagonal pattern onto which one can map orthographic projections of all five Platonic solids. Note that this figure can also be expressed in the form of an actual cube, which sixteen (doz. 14) spheres instead of thirteen circles.

It looks like the hexagonal zeitgeist is finally floating to the surface of our collective media environment. Two stories in particular off of our hexagonal news feed caught my eye this morn:

Geometry lessons
". . . Just as the 1950s will always be remembered as the decade of atomic-inspired motifs, so may the early decades of the 21st century be remembered, by those of pop cultural bent, as belonging to the hexagon."

The Hexagon Harley 1.4301
"Six is the magic number on this handcrafted custom Harley Davidson by Horst Dzhangmen. Everything but the engine, a HD Shovelhead 1340 cm3 and the frame, has been cut and built into perfectly shaped hexagons and this exceptional work took its creator three years of hard work to achieve this perfection."

The following video came to my attention recently. It presents, in my view, a perfect example of the sort of world-class hexagonal education we once provided our children in that bastion of cultural exceptionalism known as the 1980s, and which seems sadly lacking from today's undoubtedly clever yet somehow less challenging children's programming:

In this image we see the symmetry group D₆ of a regular hexagon. The hexagon can be rotated six ways, and reflected six ways. Note that any combination of two or more of these operations will still result in one of these twelve configurations.

The following is a brief survey of some elemental properties of hexagons, and why they might be useful. It is not intended to be a comprehensive treatment of the subject. My specific concern here is with the mathematical properties of hexagons, and, to an extent, their role in the natural world. I have avoided discussing hexagons as they pertain to human culture, religion, history, and other "local" concerns, though there are many fascinating instances of hexagonality and sixness in these areas, and they will no doubt be treated more fully elsewhere at another time.

Interesting article from Science's popular science outfit about the Saturnine hexagon. While it is certainly an intriguing development, and a step forward from the well-known "spinning bucket" experiments, they should get back to us when they've made a hexagon 15,000 miles wide that lasts for 30 years. (Which, for practical purposes, one wouldn't expect any time soon.) Fluid dynamics can be vastly different at different scales. I would also like to know what the viscosity is of this "water" they speak of relative to the atmosphere of Saturn.