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Is there really enough mathematical content here, beyond the pretty pictures (and they are quite pretty) to justify an article? Doing a search for some external links to justify including it, I found:
Google Scholar turned up a few more:
And, excluding other pages that seemed to be copies of links to here or MathWorld, that was pretty much it. Not promising for a page that seems to intend to be about mathematics. The mathematical content seems to be limited to: some people thought the Reuleaux triangle could be generalized in this way, but it turned out to be a mistake. Is that enough?
— David Eppstein 07:02, 12 September 2006 (UTC)
Would I be correct in surmising that there woukd be an equivalent Reuleaux and Meissner shape for each the other four platonic solids? — Preceding unsigned comment added by 64.121.1.13 ( talk) 01:10, 31 August 2020 (UTC)
The article explains that the Meissner tetrahedron is three-dimensional object of constant width. However, because it has three of its six edges rounded a bit, it has no tetrahedral symmetry.
I recently came across what appears to be a self-published paper from 2012 by a fellow named Patrick Roberts, who proved that it is possible to create a constant-width tetrahedron that is perfectly symmetric. There is also a web page with a link to the paper here: http://www.xtalgrafix.com/Spheroform2.htm
I found this fascinating, and I would like to mention this object in the article, but due to the original-research nature of the paper, I thought I'd ask here first.
@ David Eppstein: you seem to be the only regular here on this talk page. What say you? ~ Anachronist ( talk) 06:22, 7 May 2022 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Is there really enough mathematical content here, beyond the pretty pictures (and they are quite pretty) to justify an article? Doing a search for some external links to justify including it, I found:
Google Scholar turned up a few more:
And, excluding other pages that seemed to be copies of links to here or MathWorld, that was pretty much it. Not promising for a page that seems to intend to be about mathematics. The mathematical content seems to be limited to: some people thought the Reuleaux triangle could be generalized in this way, but it turned out to be a mistake. Is that enough?
— David Eppstein 07:02, 12 September 2006 (UTC)
Would I be correct in surmising that there woukd be an equivalent Reuleaux and Meissner shape for each the other four platonic solids? — Preceding unsigned comment added by 64.121.1.13 ( talk) 01:10, 31 August 2020 (UTC)
The article explains that the Meissner tetrahedron is three-dimensional object of constant width. However, because it has three of its six edges rounded a bit, it has no tetrahedral symmetry.
I recently came across what appears to be a self-published paper from 2012 by a fellow named Patrick Roberts, who proved that it is possible to create a constant-width tetrahedron that is perfectly symmetric. There is also a web page with a link to the paper here: http://www.xtalgrafix.com/Spheroform2.htm
I found this fascinating, and I would like to mention this object in the article, but due to the original-research nature of the paper, I thought I'd ask here first.
@ David Eppstein: you seem to be the only regular here on this talk page. What say you? ~ Anachronist ( talk) 06:22, 7 May 2022 (UTC)