What do you call a 3D rectangle?

[Achernar]

*Originally posted by r_k *
“Box” is just silly. A box is a physical object, which may or may not be cuboid in shape (eg think of a hat box, which is cylindrical). “Box” is certainly not a mathematical term, unless in some kind of horribly dumbed-down school textbook that doesn’t want to scare the little darlings with proper words.

Hmph. Well I think it’s hella tight.

A pyramid is also a physical object.

Nobody but Dolly bloody Levi uses hatboxes.

Box

So nyah.

[Colophon]

I just followed your link, Achernar. It said “Box: see cuboid.” So nyah right backatcha.

I half hoped that under “cuboid” it would say “see box”, but it doesn’t…

[MC_Master_of_Ceremonies]

A parallelpiped is a box whose faces are paralleograms, a cuboid is the name for a rectangular parallelpiped (i.e. one whose faces are all rectangular or square).

[Hari_Seldon]

*Originally posted by r_k *
**“Box” is just silly. A box is a physical object, which may or may not be cuboid in shape (eg think of a hat box, which is cylindrical). “Box” is certainly not a mathematical term, unless in some kind of horribly dumbed-down school textbook that doesn’t want to scare the little darlings with proper words.

Ahem, rant over.

Anyway, the mathematical term for “a geometric solid whose six faces are rectangles” (definition from Collins English Dictionary) is “cuboid”. It is a special case of the parallelepiped - also called a rectangular parallelepiped (note spelling, which I got wrong too in my last post!) **

Spelling noted. But the comment about “box” not being a mathematical term is just ignorance. Mathematicians will use whatever term they find convenient. Check out, for instance, the “box topology” on a product of spaces (usually infinitely many). And if I happened to want to talk about rectangular parallelepipeds, I would certainly call them boxes, since I much prefer one syllable to ten. Has nothing to do with dumbing down. You might be amazed at some of the common words mathematicians use in a technical sense.

I have never heard “cuboid”, but it is not unreasonable. I don’t much like it on esthetic grounds, but that is purely personal.

[The_Griffin]

surely there’s 2 different types.

1. square looking from the ends but not a cube because it’s longer in one direction

2. all directions are different lengths

[Trigonal_Planar]

I was looking for the general case of a 6-sided object, all sides at right angles, with no specifications as to size.

[The_Ryan]

An even more general term is “k-cell”. A 1-cell is a line segment, a 2-cell is a rectangle, a 3-cell is a box, a 4-cell is four dimensional box, etc.

r_k:
Do you have a problem with such words as “ball”, “handle”, “cover” and “atlas”?

[Trigonal_Planar]

Oh, I’d just like to point out that I think “box” is a perfectly acceptable term.

[The_Ryan]

Another factor that mathematicians consider is whether the interior and/or boundary is included. I think a “box” is usually just the boundary, while a k-cell is both. I don’t know of anything that refers to just the interior ( a ball is just the interior, but that’s round).