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It was obviously designed to be a cunning way of limiting the expansion of the military-industrial complex; they can't just keep building adjacent pentagons bec
by jpfed 10y ago
It was obviously designed to be a cunning way of limiting the expansion of the military-industrial complex; they can't just keep building adjacent pentagons because they don't tesselate.
- JackFr 10y agoI had always assumed it was the single exposed face of a mostly subterranean dodecahedron.
- fdej 10y agoThat is correct, but the subterranean dodecahedron itself is merely the portal that the interdimensional lizard beings use to move between our world and the 4-dimensional hyperdodecahedron.
- carlob 10y agoYour comment made me check if it actually was possible, and what the platonic solids in higher dimensions were. http://math.ucr.edu/home/baez/platonic.html http://math.ucr.edu/home/baez/platonic.html https://en.wikipedia.org/wiki/120-cell https://en.wikipedia.org/wiki/120-cell
- iMark 10y agoBut they do in 3 dimensions. Is the future of the Pentagon the Dodecahedron?
- milkytron 10y agoThe Pentagon might actually just be the top face of the massive subterranean Dodecahedron.
- thaumasiotes 10y agoI don't see the problem with including the occasional courtyard among adjacent pentagons, though.
- logfromblammo 10y agoThey would be building adjacent hexagons, to follow the curvature of the Earth. There would be at most 11 other pentagons.
- viewtransform 10y agoFor those who don't get this - it is a clever reference to Euler's Twelve Pentagon theorem : "any closed polyhedron composed no polygons other than hexagons and pentagons and having no holes must have exactly 12 pentagons."
- klodolph 10y agoPerhaps the military was a fan of Roger Penrose, and really did want to expand. Or perhaps they intended to tile the entire world with a geodesic grid.
- stronglikedan 10y agoThey can just keep adding concentric rings, and the military-industrial complex expands exponentially with each new one.
- Someone 10y ago(Pedantic/educational): quadratically (ignoring the bending of spacetime due to the mass of the military-industrial complex)
- xvedejas 10y agoThat's also assuming that the thickness of each ring is constant. If they increased the thickness by a certain percentage relative to the previous band, then you'd have exponential growth.
- Someone 10y agoBut the existing rings are equal-width, and wider rings do not make sense (the buildings would get less and less daylight)
- xvedejas 10y agoFair point. I guess there's another assumption, that the rings are built at a constant rate. In fact, if we make the typical assumption that the economy grows exponentially (which might hold for all but the longest term models), it could be possible to build newer rings at an exponentially faster speed by constructing more and more of them simultaneously.
- shalmanese 10y agoeven more pedantically: sub-quadratically since it's being built on a positively curved manifold. As the Pentagon approaches the size of a hemisphere, growth will stop and then reverse.
- Arizhel 10y agoIf they wanted to add concentric rings, then they screwed up big-time by sticking the thing next to a river. Though with the military budget, rerouting the river shouldn't be that hard to do. But the river also constitutes the boundary between Virginia and DC, so there may be political problems with that.