The title pretty much sums it up. By “three dimensional rectangle”, I mean the shape formed by taking a rectangle and extending it along the z-axis.
Three dimensional circle = sphere
Three dimensional square = cube
Three dimensional rectangle = ???
A Google search brings up “rectangular box” and “rectangular parallelepiped”, but these both seem to lack a particular je ne sais qua.
Cuboid?
The general term for such a shape is rectangular prism.
That’s what they taught me at school; I think rectangular prism may be more popular the other side of the pond, or just more popular nowadays, or maybe my maths teachers were just wrong.
If all else fails, you could borrow our “Quader”.
a rectangular parallelepiped is what I’ve always called it.
Looks like we’re right and the Yanks are wrong 
http://mathworld.wolfram.com/Cuboid.html
On a serious note, I was under the impression that ‘prism’ more properly referred to optical matter rather than geometric shapes?
(Oh, ‘cuboid’ is also an adjective…which surely beats ‘rectangular parallelepipedular’ in the usability stakes 
)
Unmodified, ‘prism’ means an optical one in everyday language, but the word does describe the shape, rather than the optical properties.
In terms of geometry, it refers to an extruded shape, so it needs a modifier; rectangular prism, hexagonal prism, etc, and of course triangular prism, the scientific term for which is The Toblerone.
Here’s some rectangular-prism type objects:
A brick.
A stick (of butter).
A slab (of concrete.)
A (mah-jong) tile.
A (stone) tablet.
A box.
A bar (of gold.)
Seems like there is no particular common term that applies generally to that shape.
If only someone would invent such a term, like… I dunno… cuboid might be good.
Perhaps, but the latter is what I would call it.
If you want to sound all mathy, you could call it D[0, 1][sup]3[/sup] (where D is an arbitrary diagonal matrix).
I’d call it a cuboid too.
Is this the end of the Anglo-American good relations?
If not the end, then the end of the beginning of the end; the beginning of the end of the beginning of the end began (or perhaps ended) when I suggested that pizza could be eaten with knife and foek, a couple of weeks ago.
And yes, it is called a foek in the Kingdom of butter.
Yes, but think how smart you’ll sound at parties!
I have to go against the cuboid tide. The word cuboid suggests it’s got equal sides and edges or at least cubelike qualities, which is not the definition of a rectangular prism. If we need a common term, rectangloid seems more accurate (although I’d be happy to assilimate quader into English).
We also could distinguish between a regular rectangloid (where four the sides are congruent and the remaining two opposite sides are square - like a stick of butter) and an irregular rectangloid (where all three pairs of opposite sides are non-conguent - like a brick).
It appears we have two proper candidates:
Rectangular Prism: I don’t like it. It requires an adjective, and is merely a description of a subset of a larger group of shapes. Its really no better than “rectangular parallelepiped”, merely 9 letters shorter.
Cuboid: This is better; it is a single word which describes the specific shape in question. There is only one problem: it suggests a “cube”, which is absolutely not the case.
I’ve decided that I like “quader”. I’m not sure of the German pronunciation, but I will be pronouncing it with a long “a”. Thank you, kellner.
So then, will there be a regular quader (stick o’ butter) and the irregular quader (brick) adopted?