| Rectangular Cuboid | |
|---|---|
| Type | Prism |
| Faces | 6 rectangles |
| Edges | 12 |
| Vertices | 8 |
| Symmetry group | D2h, (*222) |
| Schläfli symbol | { } x { } x { } |
| Coxeter-Dynkin diagram | |
| Dual polyhedron | Rectangular fusil |
| Properties | convex, zonohedron, isogonal |
In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism. The term "rectangular or oblong prism" is ambiguous. Also the term rectangular parallelepiped or orthogonal parallelepiped is used.
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. The cube is a special case of the square cuboid in which all six faces are squares.
If the dimensions of a cuboid are a, b and c, then its volume is abc and its surface area is 2ab + 2ac + 2bc.
The length of the space diagonal is
Cuboid shapes are often used for boxes, cupboards, rooms, buildings, etc. Cuboids are among those solids that can tessellate 3-dimensional space. The shape is fairly versatile in being able to contain multiple smaller cuboids, e.g. sugar cubes in a box, boxes in a cupboard, cupboards in a room, and rooms in a building.
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.
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