Pentastar & pentastar gap

pentastar1

Pentastar gap = θ
0.12838822… radians

7.356103172453456846229996699812179815034215504539741440855531 DEGREES

Pentastar Gap: This little known 7.356103 degree gap has been a key part of our analysis of numbers, geometries, chaos, quantum fluctuations, and human will.  Is it possible that this little gap could be the basis for diversity, creativity, openness, indeterminism, uniqueness and chaos? [1]

History:  Aristotle had it wrong [2]; he claimed he could perfectly tessellate the universe with it. However, if you have five perfectly shaped tetrahedrons, it is easily observed. That gap is a seminal shape. Tetrahedrons have four vertices. Octahedrons have six. Five regular tetrahedrons have seven vertices. Cubes have eight.

The gap appears to be a transcendental, non-repeating, and never ending number. The tetrahedron and the octahedron create a whole, ordered, rational, and perfect object that can perfectly tile and tessellate the entire universe.

The indeterminate and chaotic, of course, reside somewhere deep within the structure of the universe. We believe that place just may begin right here.

Here may well be the basis for broken symmetries. Of course, for many readers, this will be quite a stretch. That’s okay. For more, we’ll study chaotic maps and the classification of discontinuities.

Pentastarterahedralclusters