2Cube

2cube, sometimes written as 2-cube, commonly refers to the 2-dimensional cube in geometry. In the language of dimension theory, a d-cube is the Cartesian product of d intervals, and the 2-cube is [0,1] × [0,1], the unit square in the plane. It has four vertices (0,0), (1,0), (0,1), and (1,1); four edges of length 1; and four right-angle corners. As a regular polygon, the square is a convex polytope with dihedral symmetry group D4, capturing its eight symmetries including rotations and reflections. Its area is 1 and its perimeter is 4. The square also serves as a fundamental building block in tessellations, computer graphics, and grid-based representations, and it can be viewed as a 2-face of the 3-dimensional cube.

In higher-dimensional contexts, the 2-cube generalizes to the 3-cube (the ordinary cube) and, more broadly, to d-cubes which form the family of hypercubes in n-dimensional space. The 2-cube thus anchors both geometric intuition for squares and serves as a stepping stone to understanding higher-dimensional polytopes.

Beyond mathematics, the term 2cube or 2Cube may appear as a brand, project name, or product title in various fields. When encountered in non-geometric contexts, the exact meaning depends on the specific organization or project being referenced. See also square, cube, and hypercube for related concepts.