# Hypercube

### (Multi-Dimensional Geometry) ###### Multi-Dimensional Geometry ## What is Hypercube?

In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to . An n-dimensional hypercube is more commonly referred to as an n-cube or sometimes as an n-dimensional cube. The term measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The hypercube is the special case of a hyperrectangle (also called an n-orthotope). A unit hypercube is a hypercube whose side has length one unit. Often, the hypercube whose corners (or vertices) are the 2n points in Rn with each coordinate equal to 0 or 1 is called the unit hypercube.

### Technology Types

communication patterncubegeometric shapemulti-dimensional geometryparallel computingpolyhedronregular polyhedronsolidspatial property

### Synonyms

11-cube12-cube13-cube14-cube15-cube16-cube17-cube18-cube20-cube21-cube24-cube25-cube30-cube32-cube35-cube36-cube40-cube42-cube45-cube48-cube50-cubeDodekeractHendekeractHypercubicK-cubeMeasure polytopeN-cubeN-dimensional cube

### Translations

Hipercub (ca)Hipercubo (es)Hipercubo (pt)Hiperkubo (eo)Hipersześcian (pl)Hipirchiúb (matamaitic) (ga)Hyperkub (sv)Hyperkubus (nl)Hyperwürfel (de)Ipercubo (it)Nadkrychle (cs)Υπερκύβος (el)Гиперкуб (ru)Гіперкуб (uk)초입방체 (ko)超方形 (zh)超立方体 (ja)

## Tech Info

Source: [object Object]
— Date merged: 11/6/2021, 1:32:50 PM
— Date scraped: 5/20/2021, 5:59:41 PM