Difference between revisions of "Cube (geometry)"
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A '''cube''', or regular '''hexahedron''', is a solid composed of six [[Square (geometry) | square]] [[face]]s. A cube is [[Platonic solid #Duality | dual]] to the regular [[octahedron]] and has [[octahedral symmetry]]. A cube is a [[Platonic solid]]. All edges of cubes are equal to each other. | A '''cube''', or regular '''hexahedron''', is a solid composed of six [[Square (geometry) | square]] [[face]]s. A cube is [[Platonic solid #Duality | dual]] to the regular [[octahedron]] and has [[octahedral symmetry]]. A cube is a [[Platonic solid]]. All edges of cubes are equal to each other. | ||
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| + | The cube is also a square [[parallelepiped]], an equilateral cuboid, and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. | ||
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==Formulas== | ==Formulas== | ||
Revision as of 10:59, 24 April 2023
A cube, or regular hexahedron, is a solid composed of six square faces. A cube is dual to the regular octahedron and has octahedral symmetry. A cube is a Platonic solid. All edges of cubes are equal to each other.
The cube is also a square parallelepiped, an equilateral cuboid, and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.
Formulas
has:
- Four space diagonals of same lengths
(
) - Surface area of
. (6 sides of areas 
.) - Volume
(
) - A circumscribed sphere of radius
- An inscribed sphere of radius
- A sphere tangent to all of its edges of radius
- A regular tetrahedron can fit in exactly two ways inside a cube
(
)
. (6 sides of areas 
.)
(
)
See also
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