Simplex

The numbers of faces in the above table are the same as in Pascal's triangle, without the left diagonal.

The total number of faces is always a power of two minus one. This figure (a projection of the tesseract) shows the centroids of the 15 faces of the tetrahedron.

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points $u_0,\dots, u_k \in \mathbb{R}^{k}$ are affinely independent, which means $u_1 - u_0,\dots, u_k-u_0$ are linearly independent. Then, the simplex determined by them is the set of points

单词	Euclidean simplex
释义	Euclidean simplex 英语百科 Simplex In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points $u_0,\dots, u_k \in \mathbb{R}^{k}$ are affinely independent, which means $u_1 - u_0,\dots, u_k-u_0$ are linearly independent. Then, the simplex determined by them is the set of points
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Euclidean simplex

Simplex