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 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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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.
  
 
==Formulas==
 
==Formulas==
 
A cube with [[edge]]-[[length]] <math>s</math> has:
 
A cube with [[edge]]-[[length]] <math>s</math> has:
* Four space [[diagonal]]s of length <math>s\sqrt{3}</math>
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* Four space [[diagonal]]s of same lengths <math>s\sqrt{3}</math>(<math>\sqrt{s^2+s^2+s^2}=\sqrt{3s^2}=s\sqrt{3}</math>)
* [[Surface area]] <math>6s^2</math>
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* [[Surface area]] of <math>6s^2</math>. (6 sides of areas <math>s \cdot s</math>.)
* [[Volume]] <math>s^3</math>
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* [[Volume]] <math>s^3</math>(<math>s \cdot s \cdot s</math>)
 
* A [[circumscribe]]d [[sphere]] of [[radius]] <math>\frac{s\sqrt{3}}{2}</math>
 
* A [[circumscribe]]d [[sphere]] of [[radius]] <math>\frac{s\sqrt{3}}{2}</math>
 
* An [[inscribe]]d sphere of radius <math>\frac{s}{2}</math>
 
* An [[inscribe]]d sphere of radius <math>\frac{s}{2}</math>
 
* A sphere [[tangent]] to all of its edges of radius <math>\frac{s\sqrt{2}}{2}</math>
 
* A sphere [[tangent]] to all of its edges of radius <math>\frac{s\sqrt{2}}{2}</math>
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* A regular tetrahedron can fit in exactly two ways inside a cube
  
 
==See also==
 
==See also==

Revision as of 12:07, 10 April 2021

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.

Formulas

A cube with edge-length $s$ has:

See also

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