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 Field: Geometry
One of the 500 most frequently viewed mathematics articles.

Square cuboid[edit]

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 (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[edit]

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[edit]

A colleague added

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


  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[edit]

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 (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..[edit]

... 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 (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)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Cuboid/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

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