![]() However, the names of higher-order hypercubes do not appear to be in common use for higher powers. Using the matrix or coordinate representation it is easy to check that all such signed permutations are in fact symmetries of the cube. ![]() As a result, the act of raising a number to 2 or 3 is more commonly referred to as " squaring" and "cubing", respectively. The collection of all such decisions is called the group of signed permutations, also known as the hyperoctahedral group. Similarly, the exponent 3 will yield a perfect cube, an integer which can be arranged into a cube shape with a side length of the base. As the hypercube begins to rotate, the blue face moves to the side and both begin to become distorted as one side moves closer to the light and another farther. For example, the exponent 2 will yield a square number or "perfect square", which can be arranged into a square shape with a side length corresponding to that of the base. Generalized hypercubesĪny positive integer raised to another positive integer power will yield a third integer, with this third integer being a specific type of figurate number corresponding to an n-cube with a number of dimensions corresponding to the exponential. A unit hypercube's longest diagonal in n dimensions is equal to n. ![]() Hypercube Vertices in Parallel Coordinates This is a four dimensional visualization of the vertices. 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. Hypercube Edges in Orthogonal Projection Indices Edges Perspective Rotate xz Rotate yz Rotate xw Rotate yw Rotate xy Rotate zw Unfortunately, your browser does not support coolness. In geometry, a hypercube is an n-dimensional analogue of a square ( n = 2) and a cube ( n = 3). For the four-dimensional object known as "the" hypercube, see Tesseract. For internetwork topology, see Hypercube internetwork topology. For the computer architecture, see Connection Machine. This article is about the mathematical concept.
0 Comments
Leave a Reply. |