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 lengths of the edges or the angles between faces, a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.

A special case of a cuboid is a rectangular cuboid, with six rectangles as faces and adjacent faces meeting at right angles. A cube is a special case of a rectangular cuboid, with six square faces meeting at right angles.[1][2]

By Euler's formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula

In the case of a cuboid this gives 6 + 8 – 12 = 2; that is, like a cube, a cuboid has six faces, eight vertices, and twelve edges. Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a square frustum (the shape formed by truncation of the apex of a square pyramid).

Quadrilaterally-faced hexahedron (cuboid) 6 faces, 12 edges, 8 vertices
Cube
(square)		 Rectangular cuboid
(three pairs of
rectangles)		 Trigonal trapezohedron
(congruent rhombi)		 Trigonal trapezohedron
(congruent quadrilaterals)		 Quadrilateral frustum
(apex-truncated
square pyramid)		 Parallelepiped
(three pairs of
parallelograms)		 Rhombohedron
(three pairs of
rhombi)
Oh, [4,3], (*432)
order 48		 D2h, [2,2], (*222)
order 8		 D3d, [2+,6], (2*3)
order 12		 D3, [2,3]+, (223)
order 6		 C4v, [4], (*44)
order 8		 Ci, [2+,2+], (×)
order 2

See also

References

  1. ↑ Robertson, Stewart Alexander (1984). Polytopes and Symmetry. Cambridge University Press. p. 75. ISBN 9780521277396.
  2. ↑ Dupuis, Nathan Fellowes (1893). Elements of Synthetic Solid Geometry. Macmillan. p. 53. Retrieved December 1, 2018.
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