Talk:Near-miss Johnson solid

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Polyhedra

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possible vertices

I'm missing something somewhere. It's "obvious" that two regular triangles cannot form a vertex with a third polygon whose angle is 2π/3 or more; and yet the vertex figure $\cos {\frac {\pi }{3}}:\cos {\frac {\pi }{3}}:\cos {\frac {\pi }{N}}$ obeys the triangle inequality for all N. Can you show me the vertex figures for 3.3.6, 3.3.7? —Tamfang 19:18, 2 April 2006 (UTC)[reply]

Sorry, I see I was wrong in listing existence merely by positive angle defects, but I missed requirement that internal angle of only face can't exceed sum of angles of the other two faces! No time now for me to check again now, so if you're happy with what you changed (that I reverted), I trust your corrections. Tom Ruen 02:19, 4 April 2006 (UTC)[reply]

Incidentally, a while ago I made a test article listing vertex figures used in the uniform and johnson solids. A better article would link them all to articles, but a bit of a pain to complete links to all the long formal names. User:Tomruen/Polyhedra_by_vertex_figures. Tom Ruen 02:29, 4 April 2006 (UTC)[reply]

vocabulary

I used the word compound for the eleven Js that contain a rotunda. Is there a better word? —Tamfang 20:39, 20 May 2006 (UTC)[reply]

Hmmmm... Looking at Johnson solid terminology, seems like augmented or augumentations may be the most general term. Tom Ruen 05:13, 21 May 2006 (UTC) ... WELL, looking again, Augmented means that a pyramid or cupola has been joined to a face of the solid in question. is limited, but seems as good as anything. Tom Ruen 05:18, 21 May 2006 (UTC)[reply]

Number of examples

As I write this, there are six examples of near-misses shown, with wikilinks to near-misses that have separate pages. Should we add more, perhaps even going for a comprehensive listing? After all, the Johnson solid page lists (and shows images of) all 92. Just a question for discussion.... RobertAustin 16:50, 30 December 2006 (UTC)[reply]

If you could explain a measure for near-misses, then it makes sense to me to create a longer table of examples ordered by that measure, or alternately subtables by symmetry type C/D/T/O/I perhaps? Tom Ruen 22:03, 30 December 2006 (UTC)[reply]

Okay, converted to data table like Johnson solids. Looks like Jim McNeil's measure is his own, unpublished besides at his website [1]. Perhaps a simpler measure would be to limit the list under some VEF count, and models that are close enough to be built with rigid models. I admit the 3 truncated Catalan solids will fail a construction test for nonplanar faces or unfoldable vertex figures (like 6.6.6)! Tom Ruen 22:30, 30 December 2006 (UTC)[reply]

Poor examples

Okay, I removed these as near-misses, since they are "too far" to be built with regular polygons. Tom Ruen 22:33, 30 December 2006 (UTC)[reply]

Okay, added back Truncated triakis tetrahedron since its on McNeil's list, but as a physical model, the regular hexagons must be nonplanar to fit. Tom Ruen 23:14, 30 December 2006 (UTC)[reply]

If you allow pentagonal distortion, though, I would think that you could use regular flat hexagons. RobertAustin 13:30, 5 January 2007 (UTC)[reply]

Agreed since that's what the truncated forms are - irregular pentagons and perfect hexagon (perfect 'red polygons in general below). I was just being conservative in the removal to here. Best to show the most exact models on the page. Tom Ruen 23:20, 5 January 2007 (UTC)[reply]

Name	verfs.	V	E	F	F4	F5	F6	Symmetry
Truncated triakis tetrahedron	4 (5.5.5) 24 (5.5.6)	28	42	16		12	4	T_d
Truncated rhombic dodecahedron	24 (4.6.6) 8 (6.6.6)	32	48	18	6	12		O_h
Truncated rhombic triacontahedron	60 (5.6.6) 20 (6.6.6)	80	120	42	12	30		I_h

Diamond/rhombic faces?

Where does this 7 sided equal area but different faced solid with 4 equalateral tringles and 3 diamonds fit in? http://www.frankchester.com/2010/chestahedron-geometry/ Is a new section needed? — Preceding unsigned comment added by 78.238.220.41 (talk) 22:24, 4 November 2013 (UTC)[reply]

Faces must be regular polygons in this list. The Chestahedron is given as a special case at Diminished trapezohedron. Tom Ruen (talk) 23:09, 4 November 2013 (UTC)[reply]

A source for more candidates

http://www.cgl.uwaterloo.ca/csk/projects/nearmisses/ Holy (talk) 18:04, 16 March 2017 (UTC)[reply]

The nerds at this wiki have a considerably expanded list of near misses that may be of interest.

https://polytope.miraheze.org/wiki/Near-miss_Johnson_solid

However, they don't mention details about what makes a "near" miss. This person (Jim something?) does, but I haven't seen this metric ("distortion" of stress maps) echoed elsewhere.

https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/jsmn.htm

https://www.orchidpalms.com/polyhedra/stress_maps.htm#Distortion

As I mention below arguing against a merge of this stub with Johnson Solid, near-misses are of extreme math-nerd interest and have connections to real-world macromolecules, music theory, etc. If you're expanding this stub, make some connections! And don't take this on unless you're a serious geometry nerd, please. There's really "something there" there, but only if you geek out severely.

-- Marc R. 2600:1700:8FDB:1800:C0F3:1294:F4E8:5CB5 (talk) 23:22, 28 July 2024 (UTC)[reply]

Explanations for near misses

The article should include explanations for why each of these is a near-miss, e.g. "The pentagons are not quite equiangular" or "The square faces are actually slightly rectangular", perhaps with some measure for just how far off of regular they are. This measure would also help for defining what does and does not belong on the list, say you include everything that's within 5% of being a true Johnson solid (comparing longest and shortest edges, or largest and smallest angles on a supposedly "regular" face), then you can have a criteria for what doesn't qualify. 75.112.52.7 (talk) 14:36, 9 October 2019 (UTC)[reply]

@75.112.52.7: Many of these figures can be built in different ways by deforming different shapes. Again, this concept is really not well-defined, and it's study is pretty much exclusively recreational. – OfficialURL (talk) 21:05, 13 April 2020 (UTC)[reply]

Merge Near-miss Johnson solid into Johnson solid

I think the article may lack sources and, the content is too short to be as own article. One thing I could propose is merging the article Near-miss Johnson solid, redirecting it, and creating a new subheading in Johnson solid. The only problem is the tables of list may be merged into a such, due to the consequence of this proposal. Dedhert.Jr (talk) 05:26, 8 June 2024 (UTC)[reply]

it's not a johnson solid ya wanker 220.233.4.11 (talk) 11:40, 13 June 2024 (UTC)[reply]

That is why I'm asking for creating a new subheading of Johnson solid. It is related, but the difference is they are failed to become Johnson solid. Dedhert.Jr (talk) 00:10, 14 June 2024 (UTC)[reply]

Johnson solid is well defined; near miss is not. To merge them would invite confusion. —Tamfang (talk) 02:37, 14 June 2024 (UTC)[reply]

I agree Tamfang 84.19.44.233 (talk) 13:59, 2 July 2024 (UTC)[reply]

Near-miss mathematical objects are their own thing. Do NOT merge.

This stub is well worth expanding. Some recent references:

(on mathematical near misses in general, and connection to real-world atoms, music, etc:

https://nautil.us/the-impossible-mathematics-of-the-real-world-236638/ )

(on near-miss Johnson solids in particular:

https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/jsmn.htm

https://cs.uwaterloo.ca/~csk/other/nearmisses/

https://polytope.miraheze.org/wiki/Near-miss_Johnson_solid

)

-- Marc R. 2600:1700:8FDB:1800:C0F3:1294:F4E8:5CB5 (talk) 22:39, 28 July 2024 (UTC)[reply]

they are their own thing, do not merge StarButterflyIsCute (talk) 14:11, 24 September 2024 (UTC)[reply]

'Oppose: 'I do not believe the articles should be merged. Near-miss Johnson Solids describe a different class of polyhedra and adding the information about them to the main Johnson Solids article would be too much information. Yellowmarkers (talk) 04:20, 27 September 2024 (UTC)[reply]

If that's the case, I close the proposal. Dedhert.Jr (talk) 03:13, 28 September 2024 (UTC)[reply]