# Cube

• regular hexahedron

type platonic solid
elements f = 6, e = 12
v = 8 (χ = 2)
faces by sides 6{4}
conway notation c
schläfli symbols {4,3}
t{2,4} or {4}×{}
tr{2,2} or {}×{}×{}
face configuration v3.3.3.3
wythoff symbol 3 | 2 4
coxeter diagram
symmetry oh, b3, [4,3], (*432)
rotation group o, [4,3]+, (432)
references u06, c18, w3
properties regular, convexzonohedron
dihedral angle 90°

4.4.4
(vertex figure)

octahedron
(dual polyhedron)

net
net of a cube
3d model of a cube

in geometry, a cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

the cube is the only regular hexahedron and is one of the five platonic solids. it has 6 faces, 12 edges, and 8 vertices.

the cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. it is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

the cube is dual to the octahedron. it has cubical or octahedral symmetry.

the cube is the only convex polyhedron whose faces are all squares.

• orthogonal projections
• spherical tiling
• cartesian coordinates
• equation in
• formulas
• doubling the cube
• uniform colorings and symmetry
• geometric relations
• other dimensions
• related polyhedra
• cubical graph