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 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
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