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Simplex - Simplices

Simplex - Simplices

Jul 18, 2023

Simplex - Simplices

  • a simplex (plural: simplexes or simplices)
  • a simplex is a generalization of the notion of a triangle (2D simplex) or tetrahedron (3D simplex) to arbitrary dimensions
  • a k-simplex is a k-dimensional polytope which is the convex hull of its k+1 vertices

Simplex - Examples

  • a 0-simplex is a point
  • a 1-simplex is a line segment (between two zero simplices)
  • a 2-simplex is a triangle (with three 1-simplices as “faces”)
  • a 3-simplex is a tetrahedron (with four 2-simplices as “faces”)
  • a 4-simplex is a 5-cell (with five 3-simplices as “faces”)