Cube root polar angle by three in order to define a cube root. With this definition, the principal cube root of a negative number is a complex number, and for instance will not be −2, but rather . This difficulty can also be solved by considering the cube root as a multivalued function: if we write the original complex number "x" in three equivalent forms, namely The principal complex cube roots of these three forms are then respectively Unless , these three complex numbers are distinct, even though the three representations of "x" were equivalent. For example, may then be calculated to
Cube only member of that group that is a zonohedron (every face has point symmetry). The cube can be cut into six identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces). The analogue of a cube in four-dimensional Euclidean space has a special name—a tesseract or hypercube. More properly, a hypercube (or "n"-dimensional cube or simply "n"-cube) is the analogue of the cube in "n"-dimensional Euclidean space and a tesseract is the order-4 hypercube. A hypercube is also called