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9-cube. In geometry, a 9-cube is a nine- dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces . It can be named by its Schläfli symbol {4,3 7 }, being composed of three 8-cubes around each 7-face.
In geometry, a cube [a] is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross.
In geometry and physics, spinors ( / spɪnər /) are elements of a complex number -based vector space that can be associated with Euclidean space. [b] A spinor transforms linearly when the Euclidean space is subjected to a slight ( infinitesimal) rotation, [c] but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It ...
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. [1] [2] Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere ...
The second-order Cauchy stress tensor describes the stress experienced by a material at a given point. For any unit vector , the product is a vector, denoted , that quantifies the force per area along the plane perpendicular to . This image shows, for cube faces perpendicular to , the corresponding stress vectors along those faces. Because the stress tensor takes one vector as input and gives ...
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 dimensions is equal to .
Hyperbolic geometry is more closely related to Euclidean geometry than it seems: the only axiomatic difference is the parallel postulate . When the parallel postulate is removed from Euclidean geometry the resulting geometry is absolute geometry . There are two kinds of absolute geometry, Euclidean and hyperbolic.
A point in three-dimensional Euclidean space can be located by three coordinates. Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer ...