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It is a part of an infinite hypercube family. The dual of a 5-cube is the 5-orthoplex, of the infinite family of orthoplexes.. Applying an alternation operation, deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the demihypercubes.
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].
An important uniform 5-polytope is the 5-demicube, h{4,3,3,3} has half the vertices of the 5-cube (16), bounded by alternating 5-cell and 16-cell hypercells. The expanded or stericated 5-simplex is the vertex figure of the A 5 lattice, . It and has a doubled symmetry from its symmetric Coxeter diagram.
Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units. The Bedlam cube is a 4×4×4 sided cube puzzle consisting of twelve pentacubes and one tetracube. The Diabolical cube is a puzzle of six polycubes that can be assembled together to form a single 3×3×3 cube.