Mosaic: Geometry

There was a third influence on the original idea that I forgot to mention in the original post: Jack Chalker’s Well World.  That was certainly the kind of nigh-infinitely diverse metasetting I was going for (see also Larry Niven’s Ringworld, for that matter.)  So I started thinking about dividing the surface of the world up into hexagon-shaped cells.  But this seemed to regular and planet-centered to at all fit with the ‘natural event’ ultimate cause. [which will, when the time comes to deliver technobabble, probably involve false vacuum collapse and the mass-energy implications of an EWG multiverse]  If this is going to be happening to the entire universe (either instantaneously or in a wave spreading at the speed of light), I need a three-dimensional shape for the cells, which meant a little research into solids that can be used to tile a three-dimensional space.

It turns out that the most interesting simple way to tile a 3D space is with the Bitruncated cubic honeycomb, in which the unit cell is a Truncated Octahedron (think a d8 with the corners cut off).  That is an interesting shape, and it turns out that for a long time it was believed to be the most efficient way of tiling 3D space in terms of the surface area required.  That led to a little more research on what the actual most efficient way known of doing this, which is something called the Weaire-Phelan structure.  If you take a look at that wikipedia page, you’ll see a note that it was used to inspire the design of the “Water Cube” at the 2008 China Olympic.  A good picture of that can be found in this article here.

Yes.  That was what I wanted my world map to look like.  If this were a quick-and-dirty project I’d probably literally just steal a wall from the Cube, drop it down on my local area map, scale to preference, and go from there.  But this isn’t a quick-and-dirty project, which means that the way to go here is all-out: model a Weaire-Phelan foam of the appropriate scale, intersect it with a sphere, and then project that sphere onto a series of flat maps, first to generate the local area, and second to count the number of cells that aren’t completely oceanic or Antarctic.  This is computer programming task #1 in the overall project, then.

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