Aunit cube, more formally acube of side 1, is acube whose sides are 1 unit long.^[1][2] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.^[3]

The termunit cube orunit hypercube is also used forhypercubes, or "cubes" inn-dimensional spaces, for values ofn other than 3 and edge length 1.^[1][2]

Sometimes the term "unit cube" refers in specific to the set [0, 1]ⁿ of alln-tuples of numbers in the interval [0, 1].^[1]

The length of the longest diagonal of a unit hypercube ofn dimensions is${\displaystyle \sqrt{n}}$, the square root ofn and the (Euclidean) length of the vector (1,1,1,....1,1) inn-dimensional space.^[2]

• Doubling the cube
• k-cell
• Robbins constant, the average distance between two random points in a unit cube
• Tychonoff cube, an infinite-dimensional analogue of the unit cube
• Unit square
• Unit sphere

• Weisstein, Eric W."Unit cube".MathWorld.

• Euclidean solid geometry
• 1 (number)
• Cubes

• Articles with short description
• Short description is different from Wikidata