Unit cube

The term unit cube or unit hypercube is also used for hypercubes, or "cubes" in n-dimensional spaces, for values of n other than 3 and edge length 1.^[1][2]

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

The length of the longest diagonal of a unit hypercube of n dimensions is ${\displaystyle {\sqrt {n}}}$, the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-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