Convex polyhedron with six faces with four edges each
This article is about polyhedra with six quadrilateral faces. For polyhedra with six rectangle faces, see rectangular cuboid. For other uses, see Cuboid (disambiguation).
In geometry, a cuboid is a quadrilateral-faced convex hexahedron (a polyhedron with six faces). "Cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube by adjusting the lengths of its edges or/and the angles between its adjacent faces. In general mathematical language, a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.[1][2]
A special case of a cuboid is a rectangular cuboid, with six rectangle faces and adjacent faces meeting at right angles. A special case of a rectangular cuboid is a cube, with six square faces and adjacent faces meeting at right angles.[1][3]
Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a right square frustum (the shape formed by truncating the apex of a right square pyramid).
In attempting to classify cuboids by their symmetries, S. A. Robinson found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects".[4]
The numbers F of faces, V of vertices, and E of edges of any convex polyhedron are related by Euler's formula: F + V − E = 2.
In the case of a cuboid, this formula gives: 6 + 8 − 12 = 2; that is, like a cube, a cuboid has six faces, eight vertices, and twelve edges.
^ abRobertson, Stewart Alexander (1984). Polytopes and Symmetry. Cambridge University Press. p. 75. ISBN 9780521277396.
^Branko Grünbaum has also used the word "cuboid" to describe a more general class of convex polytopes in three or more dimensions, obtained by gluing together polytopes combinatorially equivalent to hypercubes. See: Grünbaum, Branko (2003). Convex Polytopes. Graduate Texts in Mathematics. Vol. 221 (2nd ed.). New York: Springer-Verlag. p. 59. doi:10.1007/978-1-4613-0019-9. ISBN 978-0-387-00424-2. MR 1976856.
^Dupuis, Nathan Fellowes (1893). Elements of Synthetic Solid Geometry. Macmillan. p. 53. Retrieved December 1, 2018.
^Robertson, S. A. (1983). "Polyhedra and symmetry". The Mathematical Intelligencer. 5 (4): 57–60. doi:10.1007/BF03026511. MR 0746897.
In geometry, a cuboid is a quadrilateral-faced convex hexahedron (a polyhedron with six faces). "Cuboid" means "like a cube", in the sense of a convex...
A rectangular cuboid is a special case of a cuboid with rectangular faces in which all of its dihedral angles are right angles. This shape is also called...
In the human body, the cuboid bone is one of the seven tarsal bones of the foot. The cuboid bone is the most lateral of the bones in the distal row of...
A cuboid fracture is a fracture of the cuboid bone of the foot. Diagnosis is by X-ray imaging, magnetic resonance imaging, or bone scan. Treatment may...
mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler...
(in the majority of cases), a box shape. A regular cuboid, in the context of this article, is a cuboid puzzle where all the pieces are the same size in...
between the calcaneus and the cuboid bone. The calcaneocuboid joint is a type of saddle joint between the calcaneus and the cuboid bone. There are five ligaments...
tarsometatarsal joints involve the first, second and third cuneiform bones, the cuboid bone and the metatarsal bones. The eponym of Lisfranc joint is 18th–19th-century...
incidence of planes and lines dihedral angle and solid angle the cube, cuboid, parallelepiped the tetrahedron and other pyramids prisms octahedron, dodecahedron...
parallelogram, and a prism of which the base is a parallelogram. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six...
fibular retinaculum. It crosses the lateral side of the cuboid and then runs underneath the cuboid in a groove that is converted into a canal by the long...
the minimum number of cuboid containers (bins) that are required to pack a given set of item cuboids. The rectangular cuboids to be packed can be rotated...
RECTANGLE U+25AE ▮ BLACK VERTICAL RECTANGLE U+25AF ▯ WHITE VERTICAL RECTANGLE Cuboid Golden rectangle Hyperrectangle Superellipse (includes a rectangle with...
and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid, a right rhombohedron, and a 3-zonohedron. It is a regular square prism...
Nutcracker fracture refers to the comminuted fracture of the cuboid bone of the foot. If treated improperly, it can lead to lateral column shortening and...
fragmentation matrix inside the grenade is commonly used, which may be spherical, cuboid, wire or notched wire. Most anti-personnel (AP) grenades are designed to...
underneath by a layer of fat. The five irregular bones of the midfoot, the cuboid, navicular, and three cuneiform bones, form the arches of the foot which...
chemical responsible for the distinctive maple syrup smell of fenugreek. Cuboid, yellow- to amber-coloured fenugreek seeds are frequently encountered in...
Global Information