In geometry, a cuboid is a hexahedron with six quadrilateral faces, eight vertices, and twelve edges. A rectangular cuboid has all right angles and opposite rectangular faces. When all edges are equal, it forms a cube, with six square faces. Other cuboid types include the parallelepiped with parallelogram faces and the rhombohedron with rhombus faces. Some cuboids have notable symmetry groups, such as the cube's Oh group and the trigonal trapezohedron with six congruent rhombi. Cuboids are convex polyhedra related by their polyhedral graphs to cubes, though some quadrilateral-faced hexahedra can be non-convex.
See also
Wikimedia Commons has media related to Hexahedra with cube topology.References
Robertson, Stewart A. (1984). Polytopes and Symmetry. Cambridge University Press. p. 75. ISBN 9780521277396. 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. 978-0-387-00424-2 ↩
Robertson, Stewart A. (1984). Polytopes and Symmetry. Cambridge University Press. p. 75. ISBN 9780521277396. 9780521277396 ↩
Dupuis, Nathan F. (1893). Elements of Synthetic Solid Geometry. Macmillan. p. 53. Retrieved December 1, 2018. https://archive.org/details/elementssynthet01dupugoog/page/n68 ↩
Robertson, S. A. (1983). "Polyhedra and symmetry". The Mathematical Intelligencer. 5 (4): 57–60. doi:10.1007/BF03026511. MR 0746897. /wiki/The_Mathematical_Intelligencer ↩