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In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles.
In geometry, a hypercube is an n -dimensional analogue of a square (n = 2) and a cube (n = 3). It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n ...
Hypercube graph. In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n -dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2n vertices, 2n – 1n edges, and is a regular graph with n edges touching each vertex.
Vectors. Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is.
The convex regular 4-polytopes are the four-dimensional analogues of the Platonic solids. The most familiar 4-polytope is the tesseract or hypercube, the 4D analogue of the cube. The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius.
OLAP cube. An OLAP cube is a multi-dimensional array of data. [1] Online analytical processing (OLAP) [2] is a computer-based technique of analyzing data to look for insights. The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three.
One of his sculptures depicts a set of monkeys joined together to form a 4-dimensional hypercube. [13] Segerman's techniques help us visualize a four dimensional world. [14] Just as the frame of a cube can cast a shadow on a flat wall, Segerman makes analogous shadows of four dimensional objects via a 3D printer.
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].