Simplex

Simplex[{p1,,pk}]

represents the simplex spanned by points pi.

Details and Options

  • Simplex is also known as point, line segment, triangle, tetrahedron, pentachoron, hexateron, etc.
  • Simplex can be used as a geometric region and graphics primitive.
  • Simplex[n] for integer n is equivalent to Simplex[{{0,,0},{1,0,,0},,{0,,0,1}}], the unit standard simplex in .
  • Example simplices where rows correspond to embedding dimension:
  • Simplex represents all convex combinations of the given points . The region is dimensional when are affinely independent and .
  • Simplex can be used in Graphics and Graphics3D.
  • In graphics, the points pi can be Scaled and Dynamic expressions.
  • Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.

Examples

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Basic Examples  (3)

A Simplex in 3D:

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And in 2D:

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Different styles applied to a simplex:

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Volume and centroid:

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Scope  (20)

Applications  (1)

Properties & Relations  (8)

Neat Examples  (1)

See Also

Point  Line  Triangle  Polygon  Tetrahedron  MeshRegion

Introduced in 2014
(10.0)