cube

Also known as 3-hypercube, regular hexahedron, 3-cube

A cube is a three-dimensional solid object in geometry. A cube has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron.

AI overview

A cube is a three-dimensional shape made up of six identical square faces connected by twelve equal-length edges, with eight corners where edges meet. Cubes are important in geometry and mathematics because they serve as a fundamental example of a polyhedron and appear frequently in everyday objects, from dice to building blocks.

AI-generated from the Wikipedia summary — may contain errors.

Key facts

Polyhedron.name: Cube
Polyhedron.image: File:Cube-h.svg
Polyhedron.type: Hanner polytope,orthogonal polyhedron,parallelohedron,Platonic solid,plesiohedron,regular polyhedron,zonohedron
Polyhedron.faces: 6 square
Polyhedron.edges: 12
Polyhedron.vertices: 8
Polyhedron.euler: 2
Polyhedron.vertex_config: 8 \times (4^3)
Polyhedron.schläfli: \{4,3\}
Polyhedron.symmetry: octahedral symmetry \mathrm{O}_\mathrm{h}
Polyhedron.dual: regular octahedron
Polyhedron.angle: 90°
Polyhedron.properties: convex,edge-transitive,face-transitive,non-composite,orthogonal faces,Rupert property: can pass through a hole with its copy,vertex-transitive
Polyhedron.surface area: 6 × side2
Polyhedron.volume: side3

via Wikipedia infobox

Wikidata facts

Image: The 11 cubic nets.svg

Show 3 more facts

Commons category: Cube
Schläfli symbol: {4,3}
Conway polyhedron notation: C

Sources (5)

via Wikidata · CC0

~25 min read

Article

21 sections

Contents

Properties
Measurement
Unit cube
Symmetry
Appearances
In popular cultures
In nature and science
In antiquity
Constructions
Representation
As a graph
In orthogonal projection
As a configuration matrix
Related topics
Construction of polyhedra
Polycubes
Space-filling
Miscellanea
See also
References
External links

{{infobox polyhedron | name = Cube | image = File:Cube-h.svg | type = Hanner polytope,orthogonal polyhedron,parallelohedron,Platonic solid,plesiohedron,regular polyhedron,zonohedron | faces = 6 square | edges = 12 | vertices = 8 | euler = 2 | vertex_config = 8 \times (4^3) | schläfli = \{4,3\} | symmetry = octahedral symmetry \mathrm{O}_\mathrm{h} | dual = regular octahedron | angle = 90° | properties = convex,edge-transitive,face-transitive,non-composite,orthogonal faces,Rupert property: can pass through a hole with its copy,vertex-transitive | surface area = 6 × side2 | volume = side3 }} A cube is a three-dimensional solid object in geometry. A cube has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron.

The cube is found in many popular cultures, including toys and games, the arts, optical illusions, and architectural buildings. Cubes can be found in crystal structures, science, and technological devices. It is also found in ancient texts, such as Plato's work Timaeus, which described a set of solids now called Platonic solids, associating a cube with the classical element of earth. A cube with unit length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured.