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Cube (geometry)

From AoPSWiki

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.

Formulas

A cube with edge-length $s$ has:

Four space diagonals of length $s\sqrt{3}$
Surface area $6s^2$
Volume $s^3$
A circumscribed sphere of radius $\frac{s\sqrt{3}}{2}$
An inscribed sphere of radius $\frac{s}{2}$
A sphere tangent to all of its edges of radius $\frac{s\sqrt{2}}{2}$

See also

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Categories: Platonic solids | Stubs | Geometry

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