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There's something about phi - Chapter 7 - Phi, the enneagram and the platonic solids

Javier Romañach

Chapter 7 of the series "There's something About phi". Video on the number phi, golden number, divine proportion or golden ratio and its relationship with the golden segments. Dedicated to the enneagram, its relation with the platonic solids, and the construction of an unknown figure for me tha I've named as the divertahedron.

Navigating the Lattice

You have no doubt played a 2D game on a grid of squares, chess or checkers for example. Not every piece moves the same way perhaps, however in principle each square has four neighbors over the edge, and four more along the diagonals.

Bishops know those diagonals...

...whereas Knights move over one and then two, at ninety degrees.  The horse-mounted cavalry has surprising moves.

Fewer casual gamers, but most ardent players, know the hexagonal grid just as well. A lot of tank games, drawing from our dark ages history, take place on a board of hexagons.

With the advent of computer games, the job of moving and tracking position, went from piece on the board, to avatar.  The games themselves went from 2D to 3D, with ever more elaborate floor plans.

However, consider the humble 2D chess board and tank wargame terrain.

What would be the 3D correlates?

The chess board suggests a 3D world of cubes, hexahedrons.

The tank game suggests a 3D world of dodecahedrons, diamond faced.  From every position in space, twelve possibilities suggest themselves.

What keyboard keys should we use?  One possibility: ERT for three "above", ASDFGH for six on the "same plane", and XCV for "three below".

When R. Buckminster Fuller took up the topic of "the will" in Synergetics, he stayed in his own namespace and shared his input in game playing terms.

Game Theory was already an accepted academic area of focus by that time, with World Game branching off as Fuller's innovation, and inheriting from War Games as well (logistics savvy and operations research).

"I always have twelve directions to choose from" Fuller explained (paraphrasing).  He imagined himself as a chess piece, an avatar in the IVM.

It is clear to me that most humans tend to think in a linear, Go-or No-go, greenlight-redlight manner. To me, will is an optionally exercisable control by mind over brain^__by wisdom over conditioned reflex-that becomes realizable when mind is adequately convinced regarding which of the 12 alternatives will produce the most comprehensively considerate vital advantage for all. (Synergetics 537.52)

In the Flextegrity system, both the 3D cubes and dodecahedrons feature together.  The cube domains encase the compression islands, interconnected by springs or struts.

Given every move from Icosahedron X may be represented by a single vector, perhaps represented in Quadray Coordinates, the game engine should allow multiple frequencies to interpenetrate, multiple webs, each with its avatar spider.

via GIPHY

Koski's Kiosk

Koski's Kiosk is great alliteration and will go forward in the literature, website or no.

Perhaps a synonym for "module" in the "tetrahedral wedge" sense, could be "kiosk". A tetrahedral voxel within a family consisting of family members E&T, S, A&B. Or these could be subway lines.

At the stations, the Kiosks appear as actual newstands with "read all about it" headlines regarding the Koski Identities. 

Picturing like Japanese anime, hypertoons with chill beats.

Zonohedron Zone

hollowed out

Another classic from Koski, an ongoing dissection of an interesting combo:  the greens are in the six IVM directions, whereas the reds come from five-fold world. You can see the reds in action, building the rhombic triacontahedron (bottom left).  The overall shape (transparent) is all reds and greens.

The colors refer to Zome, the construction kit, and the screenshot above is from vZome or the virtual Zome builder.  It's a standalone Java application.  Feel free to grab.

One of David's fascinations has been breaking down all these tetravolumes into sums of phi-scaled modules, the S and E modules in particular.  You'll find out more about these tetrahedrons in this blog and elsewhere.

filled in

Hypertoons on 3DTV

I've usually shared hypertoon reveries as a flat screen experience, as if on an HDTV.  You'll find an earlier blog post on LCD aesthetics.  However we need not confine our imaginations to such prosaic devices.  Won't 3DTV be here soon?

When you imagine a pixelated surface, do you think of squares or hexagons?  We can tell a lot about your personality based on that, just kidding.  As when tiling a bathroom floor, we have our reasons for going with one or another tiling pattern.

Space comes with "tiling" patterns too.  Instead of pixels, we have voxels?

When you imagine a voxelated volume, do you think of cubes or rhombic dodecahedrons?  I'd say a majority will think of cubes and don't know much about that other thingamajiggy.

However rhombic dodecahedrons are more neighborly in the sense of sharing more faces.  Cubes share six faces with neighbors (why we call them hexahedra).  Dodecahedrons (of this space-filling voxel kind) share twelve.

As soon as you start filling space with some repeated shape, you're likely to think "honeycomb" or even "lattice" whereas an engineer might think "space frame".  Different professions teach different words, but we all know what it means to "brick a volume" with some shape, even if said shape has all diamond faces.

The sculptors at Flextegrity Labs, the informal name for your builders' skunkworks, know all about modeling sculptures in 3D, given C6XTY and its progenitors came from a 3D imagination in the first place, via CAD and industrial processing.

Having the CCP (another name for our lattice, not a political party) pre-implemented in software, with each icosahedron or ball position selectively illumined, is a kind of 3DTV in its own right.

The sculpture supports its own weight.

We don't need to wait, to experiment with sound and light shows.  Our gallery was in the nightclub district, after all.

Who knows, perhaps 3D hypertoons could be in our future?

Or shall we say 4D, switching to the Bucky brand, wherein the Tetrahedron anchors our sense of "dimension" in a four directional volume, our "space"?  We've learned that "namespaces" coexist and that an either/or mindset may be unnecessary in the long run.

So sure, 4D it is.  Too.