Search results
Results from the WOW.Com Content Network
The hypercubes are one of the few families of regular polytopes that are represented in any number of dimensions. [8] The hypercube (offset) family is one of three regular polytope families, labeled by Coxeter as γ n. The other two are the hypercube dual family, the cross-polytopes, labeled as β n, and the simplices, labeled as α n.
The two general forms of the hypercube honeycombs are the regular form with identical hypercubic facets and one semiregular, with alternating hypercube facets, like a checkerboard. A third form is generated by an expansion operation applied to the regular form, creating facets in place of all lower-dimensional elements.
A hypercube is basically a multidimensional mesh network with two nodes in each dimension. Due to similarity, such topologies are usually grouped into a k-ary d-dimensional mesh topology family, where d represents the number of dimensions and k represents the number of nodes in each dimension. [1] Different hypercubes for varying number of nodes
In graph theory, the hypercube graph Q n is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q 3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Q n has 2 n vertices, 2 n – 1 n edges, and is a regular graph with n edges touching each vertex.
Alternation of the n-cube yields one of two n-demicubes, as in this 3-dimensional illustration of the two tetrahedra that arise as the 3-demicubes of the 3-cube.. In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγ n for being half of the hypercube family, γ n.
The same principle can be applied to the All-Reduce operations, but instead of concatenating the messages, it performs a reduction operation on the two messages. So it is a Reduce operation, where all processing units know the result. Compared to a normal reduce operation followed by a broadcast, All-Reduce in hypercubes reduces the number of ...
In this tiling of the plane by congruent squares, the green and violet squares meet edge-to-edge as do the blue and orange squares. In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.
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 ...