Simplex

In geometry, a simplex or n-simplex is an n-dimensional analogue of a triangle. Specifically, a simplex is the convex hull of a set of (n + 1) affinely independent points in some Euclidean space of dimension n or higher (i.e., a set of points such that no m-plane contains more than (m + 1) of them; such points are said to be in general position).

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A regular simplex is a simplex that is also a regular polytope.

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For example, a 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron (in each case with interior).

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The convex hull of any m of the n points is also a simplex, called an m-face. The 0-faces are called the vertices, the 1-faces are called the edges, the (n − 1)-faces are called the facets, and the sole n-face is the whole n-simplex itself. In general, the number of m-faces is equal to the binomial coefficient C(n + 1, m + 1).

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Geometry: Geometry (Greek Γεωμετρια, geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. It was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric c...

Convex hull: In mathematics, the convex hull or convex envelope for an object or a set of objects is the minimal convex set containing the given objects. It is the minimal convex set because the convex hull is a subset of any convex set which contains the given objects....

Affinely independent: REDIRECT Affine transformation...

Simplex related Images and Photos (experimental)

Simplex Ironer 1915