Simplex

From Citizendium
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

A simplex is a mathematical object, analogous to a triangle. Every simplex has a dimension, which is a nonnegative integer; an n-simplex means a simplex of dimension n.

  1. A 0-simplex is just a point.
  2. A 1-simplex is an interval or line segment.
  3. A 2-simplex is a filled-in triangle.
  4. A 3-simplex is a solid tetrahedron.
  5. The standard n-simplex is the set of points for which . For example, the standard 3-simplex is the shape of the corner of a cube if it is sliced off at an angle to produce a solid with three similar triangular faces (parts of the sides of the cube) and one larger, equilateral triangular face.