A **cube** is the 3-dimensional hypercube. It is also the only platonic solid that can perfectly tessellate space by itself in a honeycomb.

It has the Schläfli symbol $ \{4,3\} $, meaning that it is made of squares, three of which meet at each vertex. It can also be represented by the Schläfli symbols $ { \{ \} }^{ 3 } $ as it is the product of three line segments, $ \{ 4\} \times \{ \} $ as it is the product of a square and a line segment (in other words, a square-based prism) and $ t\{ 2,4\} $ as it is a truncated Square Hosohedron.

## Structure and sections=Edit

The cube is composed of many squares stack on each other. It is composed of two parallel squares linked by a ring of four squares. Three squares join at each corner.

When viewed from a square face, it appears as a constant sized square. When viewed from an edge, it looks like a line expanding to a rectangle and back. Finally, when viewed from a corner, it is a point that expands into an equilateral triangle, then truncates to various hexagons, then goes back to a triangle (oriented the other way) which then shrinks.

### Hypervolumes Edit

- vertex count = $ 8 $
- edge length = $ 12l $
- surface area = $ 6l^2 $
- volume = $ l^3 $

### Subfacets Edit

- 8 points (0D)
- 12 line segments (1D)
- 6 squares (2D)

### See Also Edit

Zeroth | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth | Eleventh | Twelfth | Thirteenth | Fourteenth | Fifteenth | Sixteenth | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Simplex | Point | Line | Triangle | Tetrahedron | Pentachoron | Hexateron | Heptapeton | Octaexon | Enneazetton | Decayotton | Hendecaxennon | Dodecadakon | Tredecahendakon | Quattuordecadokon | Quindecatradakon | Sexdecateradakon | Septendecapetadakon |

Hypercube | Point | Line | Square | Cube
| Tesseract | Penteract | Hexeract | Hepteract | Octeract | Enneract | Dekeract | Undekeract | Dodekeract | Tredekeract | Quattuordekeract | Quindekeract | Sexdekeract |

Cross | Point | Line | Square | Octahedron | Tetrarss | Pentarss | Hexarss | Heptarss | Octarss | Ennearss | Decarss | Hendecarss | Dodecarss | Tredecarss | Quattuordecarss | Quindecatrarss | Sexdecaterarss |

Hypersphere | Point | Line | Circle | Sphere | Glome | Hyperglome | Hexaphere | Heptaphere | Octaphere | Enneaphere | Decaphere | Hendecaphere | Dodecaphere | Tredecaphere | Quattuordecaphere | Quindecatraphere | Sexdecateraphere |