simplex - meaning and definition. What is simplex
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What (who) is simplex - definition

GENERALIZATION OF THE NOTION OF A TRIANGLE OR TETRAHEDRON TO ARBITRARY DIMENSIONS
Simplices; Affine simplex; Affine chain; Singular simplex; Simplex (mathematics); Simplicial; Simplex (abstract); Unit simplex; Standard simplex; Singular n-simplex; 2-simplex; Hypertriangle; N-simplex; 11-simplex; 12-simplex; 15-simplex; 14-simplex; 13-simplex; 16-simplex; 17-simplex; 18-simplex; 19-simplex; Euclidean simplex; 20-simplex; Simplex (geometry); Singular simplices functor; Regular simplex; Face of a simplex
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  • The numbers of faces in the above table are the same as in [[Pascal's triangle]], without the left diagonal.
  • The four simplexes which can be fully represented in 3D space.
  • The total number of faces is always a [[power of two]] minus one.  This figure (a projection of the [[tesseract]]) shows the centroids of the 15 faces of the tetrahedron.

simplex         
1. <communications> Used to describe a communications channel that can only ever carry a signal in one direction, like a one-way street. Television is an example of (broadcast) simplex communication. Opposite: duplex. 2. <algorithm> The simplex method. (2001-07-21)
simplex         
¦ adjective technical
1. composed of or characterized by a single part or structure.
2. (of a communication system, computer circuit, etc.) only allowing transmission of signals in one direction at a time.
¦ noun a simple or uncompounded word.
Origin
C16: from L., lit. 'single', var. of simplus 'simple'.
Simplex         
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope made with line segments in any given dimension.

Wikipedia

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example,

  • a 0-dimensional simplex is a point,
  • a 1-dimensional simplex is a line segment,
  • a 2-dimensional simplex is a triangle,
  • a 3-dimensional simplex is a tetrahedron, and
  • a 4-dimensional simplex is a 5-cell.

Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points u 0 , , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 u 0 , , u k u 0 {\displaystyle u_{1}-u_{0},\dots ,u_{k}-u_{0}} are linearly independent. Then, the simplex determined by them is the set of points

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

The standard simplex or probability simplex is the k − 1 dimensional simplex whose vertices are the k standard unit vectors in R k {\displaystyle \mathbb {R} ^{k}} , or in other words

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.

Examples of use of simplex
1. Health food Defatty is potent for simplex obesity which has not high lipid in blood.
2. Glaxo makes one of three drugs for genital herpes, which is caused by herpes simplex virus types 1 or 2.
3. It will employ more than 350 workers at the peak of construction. «We are excited to have Simplex Infrastructures onboard.
4. Simplex Infrastructures won the contract worth in excess of AED168 million against eight other companies based on their experience and competitive proposal.
5. Fifty–three year old Gest is claiming that Miss Minnelli hid herpes simplex, a sexually transmitted infection, from him until after their marriage.