Английская Википедия:Cuboid
Шаблон:Short description Шаблон:Other uses 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 Шаблон:Mvar, of vertices Шаблон:Mvar, and of edges Шаблон:Mvar of any convex polyhedron are related by the formula <math display=block>F + V - E = 2.</math> In the case of a cuboid this gives Шаблон:Nowrap; 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 | ||||||
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Файл:Hexahedron.png | Файл:Cuboid no label.svg | Файл:TrigonalTrapezohedron.svg | Файл:Trigonal trapezohedron gyro-side.png | Файл:Usech kvadrat piramid.png | Файл:Parallelepiped 2013-11-29.svg | Файл:Rhombohedron.svg |
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) |
Шаблон:Math order 48 |
Шаблон:Math order 8 |
Шаблон:Math order 12 |
Шаблон:Math order 6 |
Шаблон:Math order 8 |
Шаблон:Math order 2 |
See also
References
External links
- Шаблон:MathWorld
- Rectangular prism and cuboid Paper models and pictures
Шаблон:Convex polyhedron navigator Шаблон:Authority control