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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] [3] Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram. Rhombohedron is a cuboid with six rhombus faces.
It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract.
It is the symmetry group of a cuboid with an S written on two opposite faces, in the same orientation. D 2h, [2,2], (*222) of order 8 is the symmetry group of a cuboid. D 2d, [4,2 +], (2*2) of order 8 is the symmetry group of e.g.: A square cuboid with a diagonal drawn on one square face, and a perpendicular diagonal on the other one.
A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6] The number of different nets for a simple cube is 11 ...
An almost-perfect cuboid has 6 out of the 7 lengths as rational. Such cuboids can be sorted into three types, called body, edge, and face cuboids. [14] In the case of the body cuboid, the body (space) diagonal g is irrational. For the edge cuboid, one of the edges a, b, c is irrational. The face cuboid has one of the face diagonals d, e, f ...
5-cube, Rectified 5-cube, 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube; 5-orthoplex, Rectified 5-orthoplex, Truncated 5-orthoplex, Cantellated 5-orthoplex, Runcinated 5-orthoplex; Prismatic uniform 5-polytope For each polytope of dimension n, there is a prism of dimension n+1. [citation needed]
In geometry, a hyperrectangle (also called a box, hyperbox, -cell or orthotope [2]), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. [3]
For example, consider the formulas for the area enclosed by a circle in two dimensions (=) and the volume enclosed by a sphere in three dimensions (=). One might guess that the volume enclosed by the sphere in four-dimensional space is a rational multiple of π r 4 {\displaystyle \pi r^{4}} , but the correct volume is π 2 2 r 4 {\displaystyle ...
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