In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it. The inside of a cube, a cylinder or a sphere is threedimensional (3D) because three coordinates are needed to locate a point within these spaces.
In geometry, the tesseract is the fourdimensional (4D) analogue of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4polytopes.
In fivedimensional geometry (5D), a 5cube is a name for a fivedimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4faces.
