# Simplex

Yao Yao on October 19, 2014

English Chinese
simplex [ˈsɪmpleks] 单纯形（这个翻译几乎毫无用处）
tetrahedron [ˌtetrəˈhi:drən] 四面体，椎体（四个三角形构成，不是圆锥）
polytope [‘pɒlɪtəʊp] 多面体
hull [hʌl] （这个不是几何术语）outer covering (of a fruit, seed, ship or tank etc.)
face 面，不过在 Simplex 这里与我们常用的面的概念有点不同
edge
vertex [ˈvɜ:teks] 顶点
vertices [ˈvɜ:rtɪsi:z] 顶点，复数

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.

Specially,

• a single point may be considered a 0-simplex
• a line segment may be considered a 1-simplex
• a triangle may be considered a 2-simplex
• a tetrahedron may be considered a 3-simplex

The convex hull of any nonempty subset of the n+1 points that define an n-simplex is called a face of the simplex. If the size of this subset is m+1, we call this face an m-face.

Specially,

• 0-faces are called the vertices
• 1-faces are called the edges
• (n−1)-faces are called the facets
• the sole n-face is the whole n-simplex itself