多面体

The polytope is a convex hull of a finite set of points in the space.
多胞体是空间中有限个点的凸包。
A regular polytope is a highly symmetrical figure whose symmetry group acts transitively on its flags.
正多胞体是一个对称性极高的图形，其对称群在它的旗上作用是传递的。
The vertices, edges, and faces of a polytope are collectively called its facets.
多胞体的顶点、边和面统称为它的面。
The dual polytope of a given polytope P is obtained by interchanging the roles of points and hyperplanes in the definition of P.
给定多胞体P的对偶多胞体是通过在定义P时交换点和超平面的角色得到的。
The Euler characteristic of a polytope is equal to the number of its vertices minus the number of its edges plus the number of its faces.
一个多胞体的欧拉特征等于它的顶点数减去它的边数加上它的面数。
A simple polytope is one in which no vertex is incident with more than two edges meeting at that vertex.
一个简单的多胞体是指没有顶点与超过两条在该顶点相交的边相邻的多胞体。
The volume of a polytope can be calculated using the Cayley-Menger determinant formula.
可以使用Cayley-Menger行列式公式计算多胞体的体积。
Every n-dimensional polytope can be decomposed into a finite number of simplices.
每个n维多胞体都可以分解为有限个单纯形。
The Schläfli symbol represents the type of a regular polytope and encodes information about its symmetries.
施莱夫利符号表示正多胞体的类型，并编码关于其对称性的信息。
The Delaunay triangulation of a point set gives rise to a polyhedral decomposition of the space containing those points.
点集的Delaunay三角剖分导致包含这些点的空间的多面体分解。