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Properties. convex, isogonal regular, Hanner polytope. In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces . It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .
A 2D orthogonal projection of a 5-cube. A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N -dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. [1]
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. 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 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. [1] The cube is the only regular hexahedron and is one of the five Platonic solids.
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 ...
The 5-cube and 5-orthoplex are the regular forms in the B 5 family. The bifurcating graph of the D 5 family contains the 5-orthoplex , as well as a 5-demicube which is an alternated 5-cube . Each reflective uniform 5-polytope can be constructed in one or more reflective point group in 5 dimensions by a Wythoff construction , represented by ...
Rectified 5-cubes. In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube . There are 5 degrees of rectifications of a 5-polytope, the zeroth here being the 5-cube, and the 4th and last being the 5-orthoplex. Vertices of the rectified 5-cube are located at the edge-centers of ...
A prismatic 5-polytope is constructed by a Cartesian product of two lower-dimensional polytopes. A prismatic 5-polytope is uniform if its factors are uniform. The hypercube is prismatic (product of a square and a cube), but is considered separately because it has symmetries other than those inherited from its factors.
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