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. | + | 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 | + | * 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> | + | * [[Surface area]] of <math>6s^2</math>. (6 sides of areas <math>s \cdot s</math>.) |
− | * [[Volume]] <math>s^3</math> | + | * [[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> | ||
+ | * 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
- 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
See also
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