Pentastar & pentastar gap

pentastar1
Pentastar gap = θ
0.12838822… radians
7.356103172453456846229996699812179815034215504539741440855531º (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, and uniqueness? [1]

History:  Aristotle had it wrong [2]; he claimed that he could perfectly tessellate the universe with tetrahedrons. 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 vertices. Cubes have eight.The progression is important.

The gap appears to be a transcendental, non-repeating, and never-ending number.

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.

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.
terahedralclusters

Pentastar
Pentastar  logo

Endnotes and Footnotes:

[1] 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.

[2] 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.  One of the best analysis is “Mysteries in Packing Regular Tetrahedra” by Jeffrey C. Lagarias and Chuanming Zong.