The most important gap of all

A closer look at the geometric gap created by five tetrahedrons all sharing a common edge.GeometricGap3
Gap = 7.356103172453456846229996699812179815034215504539741440855531+ degrees

 Related key pages:
1. Numbers: 2016
2. Pentastar: 2017
3. Duped: 2020
2. A homepage: 2020
5. Zoomtool question: 2016
6. Inquiry for FQXi-related study: 2020

Open questions about this gap:
1. When does the first gap appear along the 202 notations?  …why?
2. There are no gaps with the initial objects, the tetrahedron and octahedron; it all fits perfectly, naturally evolving from cubic-close packing of equal spheres
3. The first time the gap is mentioned within this website:

Another look!
Our earliest comments in 2013
The perfect pentagon