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Mathematics-Online lexicon:

Simplex


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A simplex $ S\subset\mathbb{R}^n$ is the convex hull of $ n+1$ points $ P_i$ which are not contained in a hyperplane of $ \mathbb{R}^n .$

$\displaystyle S = \{ x =\sum_{j}\alpha_j p_j\,,\,
\sum_{j}\alpha_j\le 1,\ \alpha_j\ge 0 \}
$

\includegraphics[width=5cm]{a_simplex1}   \includegraphics[width=6cm]{a_simplex2}
n=2   n=3

A simplex in $ \mathbb{R}^2$ is a triangle and in $ \mathbb{R}^3$ a simplex is a tetrahedron.

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  automatically generated 8/ 4/2008