Theobald Grundhoefer, Julius-Maximilians-Universität Würzburg, Germany

Homepage(s): JMUW, Managing editor, “Advances in geometry“, Publications, The Classical Fields, Cambridge University Press, 2007, Research: Bruhat–Tits buildings role in p-adic Lie groups groups and the theory of symmetric spaces in theories of Lie groups.

Second email: 13 October 2024

Dear Prof. Dr. Theo Grundhöfer:

That recent introductory email (just below) seems too tight; let me loosen it up a bit. Obviously “gap geometries” describe an array of phenomena. I’d like to focus on “the first gap” which may well be within the first seconds of the universe. And, I believe the five tetrahedral gap might be it. Might we continue the discussion that Lagarias and Zong have opened up? -Bruce aka bec

First email: 10 October 2024

Dear Prof. Dr. Theobald Grundhoefer:

A few scholars are aware of the five tetrahedral gap; the AMS cited Lagarias and Zong with the Conant Awards in 2015 for the article,  “Mysteries in Packing Regular Tetrahedra.” Even fewer scholars are aware of a five octahedral gap.  Here it is pictured between a tetrahedral gap on the top and bottom: https://81018.com/15-2/

Might it be significant? I can find no articles about it.

Thank you.

Most sincerely,

Bruce

PS. Another rather basic insight is the answer to the question of foundational structures: What perfectly fills a tetrahedron?  What perfectly fills an octahedron?  Please see: https://81018.com/tot-2/

Postscript, 12 October 2024: That seems too tight; let me loosen it up a bit. Obviously “gap geometries” describe an array of phenomena. I’d like to focus on “the first gap.” I believe the five tetrahedral gap might be it. Might we continue the discussion that Lagarias and Zong have opened up? -bec