Double tet (Cube)

Here we have a little closer look at what is a common occurrence in nature. As we have stated previously a cube is inherently unstable. It requires triangulation for stability. From the Syergetic POV what is happening is that 2 tetrahedra tend to combine to form the cube. Once we provide the necessary triangulation with the two tetrahedra the external vertices form the cube.
If we consider the edges of the tetrahedron as unit length (2), then the edge of the cube becomes the square root of 2, an irrational number!

Now consider this; all of the geometric shapes you have seen here are related to each other by simple integer multiples, except the cube. The cube is related to the other figures through an irrational number. And, here’s the point; our entire system of mensuration is based on that single unit, square edge, x,y,z coordinate system. So every time we do any measuring of virtually any physical quantity we require compromises like “rounding off” which leave miniscule left over amounts unaccounted for. How does a soap-bubble round off and what does it do with the leftover?

Next we’ll see why a 60 degree, 4 dimensional system can help us avoid some major pitfalls.

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