# Simplex

概念挺简单，主要是生单词太多了，mark 一下。

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 | 边 |

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

*-dimensional polytope which is the convex hull of its*

**k***vertices.*

**k+1**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

*-simplex is called a*

**n****face**of the simplex. If the size of this subset is

*, we call this face an*

**m+1***-face.*

**m**Specially,

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

## Comments