Cuboid
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In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "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 and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.[1]Template:R/superscript[2]Template:R/superscript
General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles.[1]Template:R/superscript[3]Template:R/superscript Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram faces. Rhombohedron is a cuboid with six rhombus faces. A square frustum is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by truncating the apex of a square pyramid. In attempting to classify cuboids by their symmetries, Script error: No such module "Footnotes". found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects".[4]Template:R/superscript
There exist quadrilateral-faced hexahedra which are non-convex.
| Image | Name | Faces | Symmetry group |
|---|---|---|---|
| File:Hexahedron.png | Cube | 6Script error: No such module "Check for unknown parameters". congruent squares | Oh, [4,3], (*432)Script error: No such module "Check for unknown parameters". order 48Script error: No such module "Check for unknown parameters". |
| File:TrigonalTrapezohedron.svg | Trigonal trapezohedron | 6Script error: No such module "Check for unknown parameters". congruent rhombi | D3d, [2+,6], (2*3)Script error: No such module "Check for unknown parameters". order 12Script error: No such module "Check for unknown parameters". |
| File:Cuboid no label.svg | Rectangular cuboid | 3Script error: No such module "Check for unknown parameters". pairs of rectangles | D2h, [2,2], (*222)Script error: No such module "Check for unknown parameters". order 8Script error: No such module "Check for unknown parameters". |
| File:Concertina tesseract cell; rhombic prism, upper.png | Right rhombic prism | 1Script error: No such module "Check for unknown parameters". pair of rhombi, 4Script error: No such module "Check for unknown parameters". congruent squares | |
| File:Usech kvadrat piramid.png | Right square frustum | 2Script error: No such module "Check for unknown parameters". non-congruent squares, 4Script error: No such module "Check for unknown parameters". congruent isosceles trapezoids |
C4v, [4], (*44)Script error: No such module "Check for unknown parameters". order 8Script error: No such module "Check for unknown parameters". |
| File:Trigonal trapezohedron gyro-side.png | Twisted trigonal trapezohedron | 6Script error: No such module "Check for unknown parameters". congruent quadrilaterals | D3, [2,3]+, (223)Script error: No such module "Check for unknown parameters". order 6Script error: No such module "Check for unknown parameters". |
| File:梯形柱.png | Right isosceles-trapezoidal prism | 1Script error: No such module "Check for unknown parameters". pair of isosceles trapezoids; 1Script error: No such module "Check for unknown parameters"., 2Script error: No such module "Check for unknown parameters". or 3Script error: No such module "Check for unknown parameters". (congruent) square(s) |
?, ?, ?Script error: No such module "Check for unknown parameters". order 4Script error: No such module "Check for unknown parameters". |
| File:Rhombohedron.svg | Rhombohedron | 3Script error: No such module "Check for unknown parameters". pairs of rhombi | Ci, [2+,2+], (×)Script error: No such module "Check for unknown parameters". order 2Script error: No such module "Check for unknown parameters". |
| File:Parallelepiped 2013-11-29.svg | Parallelepiped | 3Script error: No such module "Check for unknown parameters". pairs of parallelograms |
See also
References
- ↑ a b Script error: No such module "citation/CS1".
- ↑ 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: Script error: No such module "citation/CS1".
- ↑ Script error: No such module "citation/CS1".
- ↑ Script error: No such module "Citation/CS1".
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