CUBOID encyclopedia topics

CUBOID - 2 reference results

In anatomy, the cuboid bone is a bone in the foot.

Cuboid

Type	Prism
Faces	6 rectangles
Edges	12
Vertices	8
Symmetry group	D_2h (*222)
Properties	convex, zonohedron, isogonal

In geometry, a cuboid (also called a rectangular prism) is a solid figure bounded by six rectangular faces: a rectangular box. 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 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 prism 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 + 2bc + 2ac.

The length of the space diagonal is $d = sqrt{a^2+b^2+c^2} .$

It is a convex polyhedron. It contains faces that enclose a single region of space. It has 6 faces, 8 vertices, and 12 edges.

Euler's formula (the number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2 gives here 6 + 8 = 12 + 2.

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, small boxes in a large box, a cupboard 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.