hexapent from Antiprism

Thinking Globally in 2016

Kirby Urner
4 min readSep 13, 2016


Since around the late 1970s, when Synergetics was first published, a small cabal, not unlike the one surrounding General Semantics (Alfred Korzybski) has continued to mix geodesic domes with spherical geometry and cybernetics, following the authors’ lead. Where did that go?

If you’re into gaming, you probably know the next version of Civilization is about to make its debut, this October. Cybernetics means games and game action, like playing chess against “The Turk” a first AI simulation, actually a little man.

The chess-playing Turk, outwardly purely mechanical, might be remembered as the Napoleon-era artifact which booted AI as a concept, given how many believed in this hoax. Nowadays we play (and/or consult) Watson and Wolfram Alpha, not little men behind the curtain.

Like many classic board games, Civilization tiles the game-playing surface with hexagons, which stretch away in a great plain, the so-called “terraform” or map. These tend to come in levels. War game simulations have been using this hexagonal motif for like forever.

As the growing cabal of Divided Spheres readers know (that’s Popko’s primer on this whole spherical geometry topic), you’ll need 12 pentagons to close this expanding plain into a ball, a real planet. The resulting pattern, the “hexapent” is what “thinking globally” now looks like.

The discovery of buckminsterfullerene in the 1980s, along with nanotubes and graphene, have revolutionized the graphic arts in favor of 60–120 degree angles. XY & XYZ grids (all 90 degrees), no longer connote “high technology.” You might study Twitter to observe these trends, or check out the Hexagonal Awareness Project, since concluded, on Tumblr.

Latitude and longitude still rely on a more XY-like grid of spherical trapezoids and as a data structure that’s fine. Juxtaposing the whole Earth with a soccer ball pattern (or higher frequency) adds a visualization layer independent of the underlying model. Either / or thinking need not apply.

So am I claiming the next release of Civilization features a hexapent design? No, I have no special insider knowledge on that score. My claim is only that I’ve been lurking on the Civilization player forums and know many gamers have been clamoring for that feature, tantamount to “going…