Geometric gap = θ
Geometric or 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, and uniqueness? 
History: Aristotle had it wrong ; he claimed that he could perfectly tessellate the universe with tetrahedrons.  We believed him for over 1800 years. However, if you have five perfectly shaped tetrahedrons, the imperfection is easily observed. That gap is a seminal shape. Tetrahedrons have four vertices. Octahedrons have six. Five regular tetrahedrons have seven or eight vertices. Cubes have eight. This progression is important.
The gap appears to be transcendental, non-repeating, and never-ending.
Of course, the tetrahedron and the octahedron together create a whole, ordered, rational, and perfect object that can perfectly tile and tessellate the entire universe.
The indeterminate and chaotic reside somewhere deep within the structure of the universe. We believe that place just may begin right here with the “Pentastar Gap.”
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, the classification of discontinuities, and quantum fluctuations. More…
Endnotes and Footnotes:
 Numbers: The first analysis within this website of the pentastar gap was done in on January 8, 2016 within an articles, “Numbers: Creating Our Universe From Scratch.” The subject was re-engaged on July 4, 2018 within an article on scientific revolutions.
 History: The first analysis within this website of the pentastar gap was done in on January 8, 2016 within an article, “Numbers: Creating Our Universe From Scratch.” The subject was re-engaged on July 4, 2018 within an article on scientific revolutions.