Simplex

In geometry, a simplex (plural simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an k-simplex is an k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points are affinely independent, which means are linearly independent. Then, the simplex determined by them is the set of points . For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron. A single point may be considered a 0-simplex, and a line segment may be considered a 1-simplex. A simplex may be defined as the smallest convex set containing the given vertices.

A regular simplex is a simplex that is also a regular polytope. A regular n-simplex may be constructed from a regular (n − 1)-simplex by connecting a new vertex to all original vertices by the common edge length.

In topology and combinatorics, it is common to “glue together” simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the word “simplex” simply means any finite set of vertices.

Read more about Simplex:  Elements, Symmetric Graphs of Regular Simplices, The Standard Simplex, Cartesian Coordinates For Regular n-dimensional Simplex in Rn, Algebraic Topology, Algebraic Geometry, Applications

Other articles related to "simplex":

Simplex - Applications
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Simplex Graph
... graph theory, a branch of mathematics, the simplex graph κ(G) of an undirected graph G is itself a graph, with one node for each clique (a set of mutually adjacent vertices ... Therefore, the simplex graph contains within it a subdivision of G itself ... The simplex graph of a complete graph is a hypercube graph, and the simplex graph of a cycle graph of length four or more is a gear graph ...
Alchip - History
... In April 2002 Cadence acquired Simplex Solutions, an ASIC design services company ... Alchip was founded six months later by Kinying Kwan and other former Simplex employees as a fabless ASIC supplier ... Simplex Solutions had gained notoriety for designing the graphics ASIC for Sony's PS2 game console ...
Bergmann Simplex
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