# On following the work of Jonathan Doye and his cluster group

References within this website:
•  In our first Wikipedia article in 2012
•  The five-octahedral gap
•  In an early article about imperfection, February 2020
•  PS, a note to Oxford scholar, Ard Louis, January 2017
The geometries of spheres, triangles… February 2018
Everything Starts Most Simply… January 2014
Oxford University, Oxford, England, UK

`Third email: November 23, 2022 Updated: 1 Feb. 2023`

Did you happen to see my two notes from this past June? Of my hundred closest geometer friends (students, faculty, professionals), nobody knew the name of our 30-sided tetrahedral-octahedral object with a gap — https://81018.com/15-2/ — so just today I tentatively named it an triantahedron

The triantahedron would have the five octahedra with five tetrahedra on top and five on the bottom.

As the professional, scholars’ scholar, would you approve?

Thank you.

Warmly,

Bruce

`Second email: June 22, 2022 at 9:22 AM`

RE: Stumbling along…
cc: Chaunming Zong, Jeffery Lagarias

Dear Prof. Dr. Jonathan Doye:

So sorry to bother you. It is barely a week since my first note!

Perhaps Professors Chaunming Zong and Jeffery Lagarias, and a few members of a polytope group (I’ve been following them for about 20 years) might have some ideas about naming conventions. If these objects have no formal name, and the gaps have no formal name, quite independent of NIST and ISO, someone within this group will know how to proceed in naming them. And, if these objects and gaps have not been studied, you all would certainly be among those who could.

Just this morning I posted a picture of the five-tetrahedrons with five octahedrons sitting on top, and five tetrahedrons sitting on top of the octahedrons. There are 15 objects sharing that centerpoint. It seems that would be the maximum number of objects to share a centerpoint. It seems logical. So what is possible with that configuration, especially with its unique gaps?

That’s this morning’s question!

Thank you ever so much.

Warmly,

Bruce

PS. The posting of the pictures are here:
https://81018.com/geometries/
https://81018.com/15-2/
https://81018.com/gap-comparison/
https://81018.com/2022/05/19/five/
Also, you might want to check on my working page about your work:
https://81018.com/doye/ I am at that point in my life where I need these little memory assists to try to stay clear about what I have said to whom! Also, so far I am coming up empty on a document and image search. …Frank and Kaspers, maybe? Thanks. -BEC

`First email: June 16, 2022, at 2:31 PM (update: 23 Nov 2022)`

Dear Prof. Dr. Jonathan Doye:

I have referenced your web resources for years now.  Although I suspect there has been no official naming of the five-tetrahedral gap, I thought that you would know. Is there a generally recognized name for that five-tetrahedral object and its gap?

Also, is there any recognition of the five-octahedral object and its gap? I am not even finding any articles about it. In May 2022, I started a little analysis: https://81018.com/geometries/ Are these configurations at all part of your studies?

And finally, most speculatively, do you know if anybody has asked the questions to see if those gaps could be related to quantum fluctuations?

Thank you so very much,

Warmly,

Bruce

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