Wikipedia:Articles for deletion/Table of polyhedron dihedral angles

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:{{la|1=Table of polyhedron dihedral angles}} – (View AfDView log | edits since nomination)

:({{Find sources AFD|title=Table of polyhedron dihedral angles}})

Even though many sources support the angle of each polyhedron, I still have no clue what's the point of its existence. Dedhert.Jr (talk) 02:11, 23 April 2025 (UTC)

• Automated comment: This AfD was not correctly transcluded to the log (step 3). I have transcluded it to Wikipedia:Articles for deletion/Log/2025 April 23. —^{cyberbot I}_{Talk to my owner:Online} 02:37, 23 April 2025 (UTC)
• Note: This discussion has been included in the list of Mathematics-related deletion discussions. WCQuidditch ☎ ✎ 02:48, 23 April 2025 (UTC)

Don’t delete this article

This article is useful 2406:B400:71:B341:E821:9E94:FF91:A0F2 (talk) 14:45, 29 April 2025 (UTC)

:

• weak keep by default, because this is a bit of a non-debate. The fact that one editor doesn't see the point of an article isn't really grounds for deletion, and the fact that someone else finds it possibly useful isn't strong grounds to keep. My feeling is that the list is apparently correct and sourced, and it's quite possible that some school kid somewhere is making polyhedron models and excited by their angles, so for the sake of them, I'm fine about the table existing in their favourite encyclopedia. Elemimele (talk) 09:53, 30 April 2025 (UTC)
• :@Elemimele If that's the case, I could barely remodel the list anytime soon. What class of polyhedra should be included in the article? And why Platonic solids, star solids, and uniform solids are included only? Catalan solids has its own list alongside with dihedral angle. Archimedean solids? Johnson solids? Dedhert.Jr (talk) 13:59, 30 April 2025 (UTC)
• ::{{u|Dedhert.Jr}} valid point: some of the main articles already tabulate dihedral angles, but others don't. The Catalan solids article does it super-clearly. I think I'd have to downgrade my weak keep to a very weak keep on the grounds that the main articles often do have the data. This is one of those deletions where I don't feel strongly enough to argue, particularly as you have much greater knowledge of the field than I. I'm a bit inclusionist when it comes to information, and don't mind lists that duplicate-and-collate numbers also available in other lists/articles, but others may feel differently. Elemimele (talk) 16:53, 30 April 2025 (UTC)
• Keep but consider at least mentioning the Dehn invariant as motivation, if not reworking/extending to a table of polyhedron Dehn invariants.
  Tables of dihedral angles for polyhedra are available from multiple sources, which goes some way towards meeting WP:NLIST. In particular, a quick WP:BEFORE search found the following two books:
• {{cite book |last1=Pugh |first1=Anthony |title=Polyhedra: A Visual Approach |date=1976 |publisher=University of California Press |location=Berkeley, CA |isbn=9780520322042 |url=https://books.google.co.uk/books?id=PmvfEAAAQBAJ}}
• {{cite book |last1=Pearce |first1=Peter |last2=Pearce |first2=Susan |title=Polyhedra Primer |date=1978 |publisher=Van Nostrand Reinhold |location=New York |isbn=9780442264963 |url=https://archive.org/details/polyhedraprimer0000pear}}

:The existing article also answers the specific issue of {{tq|What class of polyhedra should be included in the article?}}: the class of edge-transitive polyhedra, as polyhedra with non-equivalent edges will typically (though not always) have multiple distinct dihedral angles. Pugh (1976) tabulates dihedral angles for the Platonic polyhedra (Table 1.34), Archimedean polyhedra (Table 2.15), {{tq|some facially regular prisms and antiprisms}} (Table 2.16), as well as their duals (Tables 4.12 and 4.13). Similarly, Pearce and Pearce (1978) tabulates dihedral angles for the Platonic polyhedra (Regular Polyhedra), Archimedean polyhedra (Semiregular Polyhedra), quasiregular polyhedra, and Catalan solids (Duals of the Semiregular Polyhedra). Out of the 13 Archimedean polyhedra, only the cuboctahedron and icosidodecahedron have uniform dihedral angles (in fact, they're isotoxal, hence are already included in the current article).

:I am sympathetic to the nominator's argument that the current article provides no good rationale for why it might be useful to tabulate dihedral angles, making it seem like an indiscriminate collection of unexplained statistics (WP:NOTSTATS). In my view, the main reason why anyone would be interested in comparing dihedral angles between polyhedra is via the theory of equidecomposability initially developed to answer Hilbert's third problem: a set of polyhedra is scissors-congruent to another set of polyhedra if they have the same volume and Dehn invariant. The Dehn invariant of a polyhedron is a function of its edge lengths and dihedral angles: Dehn invariant#Examples lists dihedral angles for the five Platonic solids, using these to calculate their Dehn invariants, as well as listing Dehn invariants (without derivation) for ten of the thirteen Archimedean solids. The MathWorld page [https://mathworld.wolfram.com/PolyhedronDissection.html Polyhedron Dissection] tabulates Dehn invariants and volumes for {{tq|sets of unit equilateral polyhedra which are interdissectable}}; it has a somewhat different inclusion criterion for polyhedra (interdissectability rather than isotoxality), but perhaps lends further weight to the argument that a more useful framing for this WP article might be in terms of dissection invariants for polyhedra.

:If we decided to move to this framing, expanding the scope of the article from isotoxal polyhedra to the full set covered by Pugh (1976) or Pearce and Pearce (1978) might be worth considering. One caveat is that {{citation |last1=Conway |first1=J. H. |author1-link=John Horton Conway |last2=Radin |first2=C. |author2-link=Charles Radin |last3=Sadun |first3=L. |arxiv=math-ph/9812019 |doi=10.1007/PL00009463 |issue=3 |journal=Discrete and Computational Geometry |mr=1706614 |pages=321–332 |title=On angles whose squared trigonometric functions are rational |volume=22 |year=1999 |s2cid=563915 }}, Table 3, p. 331. only covers {{tq|Dehn invariants for the non-snub Archimedean polyhedra of edge lengths 1}}, so we might need to dig up another reference to cover the rest of these polyhedra.

:A less dramatic change (that might be less disruptive / work better in practice) might be to keep the current scope but mention the Dehn invariant as motivation. E.g. the supplementary dihedral angles of tetrahedra and octahedra explain why it's possible to fill space with them (as the tetrahedral-octahedral honeycomb). I'd be keen to hear others' thoughts on these suggestions. Preimage (talk) 16:03, 2 May 2025 (UTC)

::Interesting. I retract my nomination for now. Dedhert.Jr (talk) 10:47, 3 May 2025 (UTC)

: Keep I was going to write a thing but everything I would have said is subsumed by {{u|Preimage}}'s compelling comment. --JBL (talk) 17:56, 2 May 2025 (UTC)

: Keep - Although I wasn't able to fully follow them, {{u|Preimage}} gave very good reasons. Itzcuauhtli11 (talk) 01:18, 7 May 2025 (UTC)

{{clear}}

:The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.