Talk:Cuboid

Square cuboid

Pardon me for being stupid, but is a square cuboid not only one square face? If it has two square faces then does its conjunction on each edge not require that the third is therefore also a square?

Care to sign your post (;-)? The sentence in the article is correct. Hint: A cuboid has six faces. But you are thinking along the right line (:-). --RainerBlome 06:36, 23 July 2007 (UTC)

From the article:

"The square cuboid, square box or right square prism (also ambiguously called square prism) is a special case of the cuboid in which at least two faces are squares."

Each face of a cuboid is identical to the opposite face. This means a square cuboid must have "at least" 2 square faces, and it must be an even number.

Sorry but in fact, a square cuboid must have AT MOST 2 square faces. The other 4 faces can be equal sized rectangles. e.g. the rectangles can measure 6cm on each length and 2cm in width therefore having the two square faces measuring 2cm on each side. — Preceding unsigned comment added by 186.45.84.40 (talk) 10:15, 2 October 2013 (UTC)

If a square cuboid has 4 square faces, then the other 2 faces must also be square, and the "square cuboid" is actually a cube in that case. User: Unregistered 18 Feb 2008

Being a cube doesn't stop it from also being a cuboid. —David Eppstein (talk) 15:39, 2 October 2013 (UTC)

The Word Itself

It says that i added

It can also be called a rectangular parallelepiped or rectangular prism.

I don't think it was bcz i was on drugs tho it would make more sense than what i remember, but i think it's wrong, bcz "rectangular" does not (for a solid figure) imply all faces. "Right rectangular prism", but i'm not sure we should bother with that.
--Jerzy·t 17:25, 27 May 2005 (UTC)

I took higher level math, and I check it on the Mathworld website.... The statement about "rectangular parallelepiped " is correct, I should be added. The current description is too "dumbed down". A Cubiod is rather technical in and of its self, therefore having the discription equally technical is justified. Ashby

Good then.

Certainly the word cuboid is technical (you can minor in math and not know it), but this is not a dictionary, and the article is not about the technical word "cuboid", but about the sometimes technical, sometimes simplistic concept of cuboid. Its only really suitable name (adequately precise and adequately brief) is "cuboid", but the technical sound of that word is a red herring: piping means it can be lk-ed via box, and inspected by non-technical users who want to know if we're ruling out a 10-faced box (its interior is the union of two truncated square pyramids) that might have a fast-food burger in it, or a cylindrical one with 3 pounds of Quaker-brand oatmeal. To see that this is not hypothetical, sample the articles that lk to this talk page's article.

I've no objection to including good rigorous material, but do bear in mind that the straight-forward stuff needs to be there too. None of these articles belong exclusively to the specialists.

--Jerzy·t 07:14, 1 Jun 2005 (UTC)

Surface area

A colleague added

, or in a shortest calculation, 2(a+b)h+ab.

but

1. They must mean "2((a+b)h+ab)
2. The h is undefined, but h=c would fix it
3. It needs some justification of the logic of "shortest": what assumption is involved as to, e.g., ratio between time do multiplications and addtiongs, and what is the domain where that matters? This isn't an optimum-computation manual, and the effort of remembering a less intuitive formula is unlikely to be repaid.

Let's hear what they have in mind here.
--Jerzy·t 05:36, 16 Jun 2005 (UTC)

Euler Brick

This didn't make any sense to me (a lowly Physicist) until I followed the link.

"A cuboid with integer edges as well as integer face diagonals is called an Euler brick, for example with sides 44, 117 and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists."

I think the words length and area are missing. But it is not my field so I have not changed it — Preceding unsigned comment added by 130.88.75.48 (talk) 09:40, 5 September 2011 (UTC)

An edge or a diagonal has length, not area. —Tamfang (talk) 04:11, 11 October 2011 (UTC)

Am I correct..

... in saying that according to the definitions given on the main page, a square cuboid is not a special case of a rectangular cuboid since the former may have 4 faces which are not rectangles, whereas the latter has all faces rectangles ? If so, is this definition of a square cuboid intended, or should a square cuboid be defined as a cuboid in which all faces are rectangles and at least 2 are squares - i.e. a rectangular cuboid of which at least 2 faces are squares ? — Preceding unsigned comment added by 77.96.59.93 (talk) 18:58, 27 November 2013 (UTC)

You seem to be under the impression that a square is not a rectangle. While there is some support for that position in the literature, I don't think it's a helpful point of view. A square is a special kind of rectangle, but it is still a rectangle. The square cuboid's square faces are also rectangles, and the square cuboid is also a rectangular cuboid. —David Eppstein (talk) 19:12, 27 November 2013 (UTC)

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Geometry guy 22:08, 22 May 2007 (UTC) A year or two ago I was looking for an english word for the notion "rectangular box" and was surprised to find such a modest article. Cuboids are so common in life that the subject fits the definition of "Top Importance": Extremely important, even crucial, to its field, and very significant beyond it. However, because cuboids are so commonplace, many people just know its important properties and do not need an encyclopedia to look them up. In this regard, the article about "cuboid" is useful mainly to associate the word with its meaning. So, for Wikipedia, the importance of the article is relevant here, not the importance of the subject. Still, since cuboids are definitely of more than specialist interest, I give this article "Medium" importance. --RainerBlome 19:59, 21 June 2007 (UTC) Judging from its age, the amount of edits, and my own impression, the article meets the important demands. Therefore I deem it a Start rather than a Stub. --RainerBlome 20:09, 21 June 2007 (UTC)

Last edited at 20:09, 21 June 2007 (UTC). Substituted at 01:56, 5 May 2016 (UTC)

Is this whole article completely wrong?

The Cuboid definition at wolfram alpha, which is linked to from this page says: A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The cuboid is also a right prism, a special case of the parallelepiped, and corresponds to what in everyday parlance is known as a (rectangular) "box."

And the text book citation on this article, to Elements of Synthetic Solid Geometry

https://archive.org/details/elementssynthet01dupugoog/page/n68/mode/2up

p53, Def. 4) says: If the three sections are rectangles, all the faces are rectangles, and all the dihedral angles are right angles, and all the corners are right corners [...] The figure is then a cuboid.

It too requires that a cuboid is rectangular.

Everywhere I look, including the sources and references on this article say a cuboid is rectangular. Its faces are rectangles (more specific than merely 'quadrilaterals' as stated). And therefore NO, a rectangular cuboid is not a special case of cuboid -- a cuboid is ALREADY rectangular, and then NO a frustrum, rhombohedron, parallelepiped, etc are NOT cuboids. 70.69.234.76 (talk) 18:35, 1 March 2024 (UTC)

So what other word do you use for the actual topic of this article, the shapes that are combinatorially equivalent to cubes but not required to have rectangular sides? It is clear that some people use "cuboid" in the restricted sense that you mean. It is also clear that some people use "cuboid" for the more general shape (example: doi:10.1007/BF03026511). What is less clear is whether there is any alternative to "cuboid" for the more general shape. —David Eppstein (talk) 19:12, 1 March 2024 (UTC)

The article you reference doi:10.1007/BF03026511 could be introducing its own local definition for its own purpose, "Suppose that we call a polyhedron a cuboid iff it is combinatorially equivalent to a cube." That, to me, seems to fall short of being a claim that this is what is generally accepted to be called a cuboid, and more of a 'lets call these solids cuboids as a convenient shorthand for our purpose here'. Is there a more authoritative source or more consensus on that usage?

As for what other word to use for the shapes in the table in this article. Both the table on this page and the same table on the more general hexahedron page ( https://en.wikipedia.org/wiki/Hexahedron ) are co-labelled "Quadrilaterally-faced hexahedron" which seems unambiguous, precise, and correct. It refers to no other polyhedra, and leaves none of the ones in the table out. 70.69.234.76 (talk) 23:06, 1 March 2024 (UTC)

Please provide evidence that this phrase is actually in common usage. I can only find a handful of hits for it in Google Scholar, several of which immediately clarify what they mean by writing "quadrilaterally-faced hexahedron (cuboid)". The fact that this name is also used for a different meaning is irrelevant; what is relevant is what name is in common use for this meaning. See WP:NOTDICT and WP:COMMONNAME. —David Eppstein (talk) 00:03, 2 March 2024 (UTC)

I'll set aside what to call quadrilateral faced hexahedra aside for a moment; because that's not really my issue.

You say "what is relevant is what name is in common usage for this meaning". Well, what mathematical name is in common usage for things are ONLY rectangular boxes and not parellelepides and frustrums? Isn't that name: "cuboid"?

Shouldn't that be clear from the article?

I could see how the article might expand from there that there are these other more exotic shapes that are sometimes also classed as cuboids, and when cuboid is used in that context then the usual 'cuboid' is a 'rectangular cuboid'.

The article cites a page from textbook on solid geometry; and it says:

"If the three sections are rectangles, all the faces are rectangles, and all the dihedral angles are right angles, and all the corners are right corners [...] The figure is then a cuboid"

Those are the mathematically defining criteria for what a shape needs to be to be a cuboid; and then wikipedia directly contradicts that and says that cuboids can have any quadrilateral shaped face at any angle.

If we consider that the parallelepiped is also cuboid based on another source, fine, but then shouldn't the fact that the source materials are in direct opposition, itself, be made apparent?

And shouldn't the FAR more common meaning of cuboid -- that of being a box and only being a box, be more clear and prominent? 70.69.234.76 (talk) 02:42, 2 March 2024 (UTC)

We have an article about the things you want to call cuboids. It is rectangular cuboid. That is not the subject of this article. This article is about the things you want to call quadrilateral-faced hexahedra. Regardless of the name, the subject of the article is what it is. See WP:NOTDICT, again. Dictionary articles are about words and their meanings. Encyclopedia articles are primarily about the things described in those articles, and to a much lesser extent about the words used to name those articles. —David Eppstein (talk) 06:19, 2 March 2024 (UTC)

This article has 4 citations:

1 - Robertson, I can't find it online. I'd love to see what it actually says.

2 - Branko - cited as re-using the word cuboid to talk about a more general class of polytopes expanded into higher dimensions.

3 - Dupuis - says a cuboid MUST be rectangular.

4 - Roberston - to me, that looks a LOT like Branko, where he literally says in a paper "Suppose that we call [these things] cuboids". I think he's appropriating the term to talk about a more general class (which is the subject of the article).

Also, hang on, that's the same Robertson -- that makes it especially interesting to me what he said in "Polytopes and Symmetry"; what does he say in polytopes and symmetry? Do you have access to that reference? can you share what it actually says?

I don't really have an issue with this article 'existing' per se. And I don't really have an issue with this article being called cuboid, if that's the common term applied to the class of shapes here, if this class of objects is referenced often enough to deserve its own article.

My issues here are that:

1) This article on 'cuboid' cites a reference that says the subject matter of this article are NOT cuboids, surely that should be called out somehow?

2) The disambiguation page for Cuboid doesn't include 'rectangular cuboid' despite that being the article most people would actually be looking for. When you search for cat, both the article for the domestic house cat, and the larger family of cats including lions and tigers are included in the disambiguation page. Not so here. Only this article is returned. I think that's also an issue.

3) Yes I know wikipedia is not a dictionary; and I understand your point - but you have one source using cuboids for quadrilateral polyhedra and one source saying those non-rectangular solids are NOT cuboids - that disagreement needs to be apparent.

The article for rectangular cuboid says "These are often called "cuboids", without qualifying them as being rectangular, but a cuboid can also refer to a more general class of polyhedra, with six quadrilateral faces" -- that's a really weak statement; that fails to reflect that MOST sources actually DEFINE cuboid to REQUIRE them to be rectangular, and that the more general class of polyhedra according to those sources would NOT be cuboids.

Interestingly the line I quoted from rectangular cuboid again a cites back to the same 1984 Robertson text. 70.69.234.76 (talk) 22:18, 4 March 2024 (UTC)

In doing a search, this use of the name 'cuboid' seems to be very rare. The only source I can find by an author other than Robertson, who seems to have coined this usage, is one 2019 PhD thesis. By contrast, I can easily find hundreds of examples of sources using 'cuboid' to mean a rectangular parallelepiped. I'd recommend putting the disambiguation page Cuboid (disambiguation) at the title Cuboid, and possibly renaming Rectangular cuboid to Cuboid (geometry). I'm not sure what the right title is for the subject of this current article under discussion. Is it really even notable as a concept? Are there other authors beyond Robertson who have anything meaningful to say about it? It could probably just be merged as a section of Hexahedron. –jacobolus (t) 23:35, 4 March 2024 (UTC)

There are plenty of examples of "cuboid" being used in the general sense in the scientific computing / finite element meshing literature. For example:

• Zienkiewicz & Phillips 1971 doi:10.1002/nme.1620030407 (see for instance fig. 7)
• Pissanetzky 1981 doi:10.1002/nme.1620170209 (see for instance figs. 6 & 7)
• Kohl 1996 doi:10.1016/0097-8493(95)00099-2 (see for instance fig. 19(e), identified as being a cuboid earlier in the text)

—David Eppstein (talk) 01:40, 5 March 2024 (UTC)

From skimming around, the name "hexahedron" seems to usually refer to the quadrilateral-faced topological cube rather than other 6-faced polyhedra, and seems much much more common for this than "cuboid". Apparently in finite element literature it's called a "brick". Edit: after more skimming, I would say that the relevance to "hexahedral mesh" construction is the main reason this shape is notable, and by far dominates all of the research literature ever mentioning it. If there's going to be an article about this, it should maybe focus on that topic. –jacobolus (t) 02:12, 5 March 2024 (UTC)

Another phrase that appears to describe the six-quadrilateral shapes in some literature is "combinatorial cube", although that also has other meanings. See e.g. arXiv:1707.06563, arXiv:2212.14721, arXiv:1912.09554. Also, "combinatorial box": doi:10.1007/978-94-011-5020-0_19. —David Eppstein (talk) 08:00, 5 March 2024 (UTC)