$\begingroup$ Show I have always thought the best name of the 3d equivalent of a rectangle was "cuboid". I am talking about the 3d shape with 6 rectangular faces shown below. However, when looking up the name of this shape, I get confusing results. Many sources including most dictionaries and geometry textbooks do list cuboid as the name. However the wikipedia article on cuboid goes out of its way to distinguish cuboid as being actually a hypernym of the target shape I describe:
The wikipedia page cites Polytopes and symmetry by Robertson, Stewart Alexander for this fact, even thought it contradicts many other geometry textbooks. If I need a way to unequivocally refer to the shape in question, do I really have to say "right cuboid" or "rectangular cuboid" every time? Or is the Wikipedia article wrong and simply reflecting some specific unconventional view of one geometer in 1933?
asked Dec 15, 2019 at 1:52
$\endgroup$ 8 $\begingroup$ The word "cuboid" is not consistently defined across all of mathematics—indeed, there are a lot of terms in mathematics which are not consistently defined. A good rule-of-thumb is that the consistency of a term's use is proportional to its frequency—that is, terms which are used more often are more likely to be used consistently. As different authors use "cuboid" to mean slightly different things, and as each of those things has other names as well, the best advice I can give is the following:
As an aside, my first impulse was to refer the shape depicted in the question as a "rectangular prism", and to think of a cuboid as something more general. The linked Wikipedia article agrees, and also suggests "rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped" for the brick shown in the question. answered Dec 15, 2019 at 18:47
Xander Henderson♦Xander Henderson 24.4k25 gold badges56 silver badges84 bronze badges $\endgroup$ $\begingroup$ Rectangular Prism, brings forth the image of a triangular prism, then the reader morphs it into a rectangle in the minds eye next. Cuboid, brings forth the image of a cube, then the reader imagines a cube-like shape. i feel the former is easier for a reader/listener to mentally picture, which the cuboid is rather ambiguous. Having said that, cuboid does feel like the more succinct way of writing, so I will opt to use "cuboid" in writing and "rectangular prism" in speech. It really does seem like a new term should be coined that listeners/readers can directly equate to the shape, rather than a stepping stone building off other known shapes. answered Feb 11, 2021 at 15:47
$\endgroup$ 2 Not the answer you're looking for? Browse other questions tagged geometry terminology math-history rectangles or ask your own question.What is a rectangle called in 3D?A prism you can view as a three-dimensional object, and since it's saying a rectangular prism, well, the best one here that is rectangular, notice, this shape right here is rectangular on every side, and it's three dimensions. It is a prism, and so this is the rectangular prism.
Is a rectangle 3D shape?2D shapes including rectangles, squares, circle and triangles. 3D shapes including cubes, cuboids, pyramids and spheres.
Is a 3D rectangle called a cube?In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cube.
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