Why does every piece of reality have exactly twelve ports?

Twelve is forced by counting, the way a twenty-sided die always has twelve corners. Each piece of the world is a closed boundary carrying ports, its points of contact with neighbors, and four conditions fix how it is cut: triangular faces; two faces along every seam; five faces ringing each port; and every loop of comparisons bounding some faces, which makes the surface a sphere. Count seam-ends and face-sides two ways each, and ports minus seams plus faces comes out as a sixth of the ports. A sphere sets that combination to two, so there are twelve ports, thirty seams and twenty faces. Thirteen fails outright, since sixty-five seam-ends cannot pair up. The twelve readings, as twelve reversible dials, split into one plus three plus eight, which is hypercharge, the weak force and the strong force.

Also in Chapter 26: Why Exactly These Forces?.