SELECTED IDEAS OF BUCKMINSTER FULLER
TETRAHEDRA
GEOMETRY
If the radii of identical close-packed atoms have a value of 1, then the distance between their centers is equal to 2.
It then follows that a basic unit vector of a tetrahedron formed by these atoms would also equal 2.
If a tetrahedron is made out of unit vectors with a value of 2, then the edges of a cube containing this tet must have a value of the square root of 2 or 1.4142136.
This is how to convert from our present artificial 90 degree cubical system of measuring to nature's much simpler 60 degree coordinate system.

For further information see:

Synergetics R Buckminster Fuller pp 588-9 1975

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