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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.
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.
5D with 4D surfaces. regular 5-polytope. 5-dimensional cross-polytope. 5-dimensional hypercube. 5-dimensional simplex. Five-dimensional space, 5-polytope and uniform 5-polytope. 5-simplex, Rectified 5-simplex, Truncated 5-simplex, Cantellated 5-simplex, Runcinated 5-simplex, Stericated 5-simplex.
The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken as a unit for hypervolume. [2] Coxeter labels it the γ4 polytope. [3] The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope.
A 5-polytope is a closed five-dimensional figure with vertices, edges, faces, and cells, and 4-faces. A vertex is a point where five or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon where three or more cells meet. A cell is a polyhedron, and a 4-face is a 4-polytope.
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C 5, hypertetrahedron, 'pentachoron, [1] pentatope, pentahedroid, [2] tetrahedral pyramid, or 4-simplex (Coxeter's polytope), [3] the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three ...
Voronoi diagram. In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called ...
The cubical graph is a special case of hypercube graph or -cube—denoted as —because it can be constructed by using the operation known as the Cartesian product of graphs. To put it in a plain, its construction involves two graphs connecting the pair of vertices with an edge to form a new graph. [30]