The Geometric Structure of Political Systems

The premise of Democracy is said completely said in the name: rule by the people. This means an upside down pyramid, except that in our case the pyramid stops short and ends in a triangle, making it more stable. Kinda neat to think about, actually. You COULD argue that the more stable the 3D object that represents your management structure is, the more stable the management structure is.
Pyramids are rigid. They are very stable, but very rigid. It requires the low base, the submission of the masses to keep aloft the point.
An inverted pyramid is completely unstable; that is, the masses are the top of the power structure, but will tip from that precarious location at a tap.
A truncated inverted pyramid, based in triangle instead of a point, has the best of the two previous systems. It keeps the individual freedom that the inverted pyramid style began with, and some of the stability of the regular pyramid.
Communism: You can imagine a flat piece of cardboard supporting a REALLY tall bottle cap. The masses stay at the bottom, but the leaders are precarious.

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Image: Carey Tilden/Wikimedia Commons, CC BY 2.0
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