Anton Betten, Colorado State University, Fort Collins

Homepage(s): CV, Google Scholar, Publications,

RE: On the problem of classification of combinatorial objects
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First email: 1 December 2022 @ 10:11 AM 

Dear Prof. Dr. Anton Betten:

You have the depth and breadth in geometry to advise us high school geometers who are stumbling around looking for someone to confirm or deny our “un-covering” of a fascinating geometry of five-tetrahedrons, over five-octahedrons, over five tetrahedrons: https://81018.com/15-2/

We are not finding it within any references. The five tetrahedral geometry has been studied a little, but not profoundly. The five octahedral geometry just appears to be overlooked. I had asked Hans Havlicek about it and he referred us to Michel Planat of The FEMTO-ST Institute in France. Michel has referred me to his work but not to any writings about this rather basic construction.

Are you familiar with it? If it is something that has been overlooked, might it be a good thing to introduce to your students at Colorado State University as well as the high school teachers within Fort Collins? 

I started my work on that five-octahedral unit in May. If it’s new, it needs to be in the hands of a professional and not a 75 year old, former high school teacher!  Thanks. 

Warmly,

Bruce

PS. My work on this modeling project actually began with an introduction to Aristotle’s mistake: https://81018.com/duperd/#Aristotle and continued with my correspondence with Zong and Lagarias, the authors of an AMS award winning publication, Mysteries in Packing Regular Tetrahedra. Six years later I finally asked (May 2022) asked myself, “What happens when five octahedron share a common centerpoint?” I quickly recognized it as a sister to the tetrahedral gap and it wasn’t too long thereafter that I started playing with models!  https://81018.com/geometries/   -BEC