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• Simplicial homology
  ...$n+1$ elements, it is called an $n$-''simplex''<!--\index{simplex}-->, or simplex of dimension $n=\dim a$. *The highest dimension of a simplex in $K$ is called the ''dimension''<!--\index{dimension}--> of $K$:
  31 KB (5,170 words) - 13:44, 1 December 2015
• Simplicial complexes and maps
  ...i-graph”). Its elements are called $0$-, $1$-, and $2$-simplices<!--\index{simplex}-->. ...identical attribute form an element of our simplicial complex, an $(n-1)$-simplex. $\square$
  27 KB (4,625 words) - 12:52, 30 March 2016
• Multilinear algebra
  ...they can cancel etc., and their signs may depend on how the regions are ''oriented'' with respect to the coordinate axes. Of course, once we start talking about ''oriented'' cells, we know it's about ''chains'', over $R$.
  49 KB (8,852 words) - 00:30, 29 May 2015
• Simplicial maps and chain maps
  ...otation.''' We allow ''repetition of vertices'' in the list that defines a simplex. A list of vertices is an $m$-simplex if there are exactly $m+1$ distinct vertices on the list.
  34 KB (5,897 words) - 16:05, 26 October 2015
• Simplicial maps
  ...otation.''' We allow ''repetition of vertices'' in the list that defines a simplex. A list of vertices is an $m$-simplex if there are exactly $m+1$ distinct vertices on the list.
  34 KB (5,929 words) - 03:31, 29 November 2015
• Discrete calculus article
  A '''simplicial complex''' <math>\mathcal{K}</math> is a set of [[Simplex|simplices]] that satisfies the following conditions: :1. Every [[Simplex#Elements|face]] of a simplex from <math>\mathcal{K}</math> is also in <math>\mathcal{K}</math>.
  27 KB (4,329 words) - 16:02, 1 September 2019
• Chain maps
  ...otation:''' we allow ''repetition of vertices'' in the list that defines a simplex. A list of vertices is an $m$-simplex if there are exactly $m+1$ distinct vertices on the list.
  47 KB (8,115 words) - 16:19, 20 July 2016
• Topology Illustrated -- Index
  *[[boundary of an oriented simplex|boundary of an oriented simplex]] *[[geometric simplex|geometric simplex]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Maps of polyhedra
  ...ty map $\operatorname{Id}:|\sigma |\to |\sigma|$ of the complex of the $n$-simplex $\sigma$. Prove that the number of simplices cloned by $g$ is odd. Hint: Wh '''Proposition.''' For every simplex $\sigma\in K^m$, there is a simplex $\tau \in L$ such that
  51 KB (9,162 words) - 15:33, 1 December 2015
• Euler and Lefschetz numbers
  ...rem holds if the ball is replaced with anything homeomorphic to it, such a simplex. under some norm so that the new prices form the $n$-simplex $\sigma$.
  41 KB (7,169 words) - 14:00, 1 December 2015
• Manifolds
  ...ditions on a complex is clear now: we have to check that the star of every simplex of every dimension forms an $n$-ball. The difficulty is that there will be ...hic to the $n$-ball are glued to each other. In other words, if an $(n-1)$-simplex is shared by three $n$-simplices, this is not an $n$-manifold.
  51 KB (8,919 words) - 01:58, 30 November 2015
• Singular chain complexes
  *copies of (oriented) $k$-dimensional [[simplices]] $\Delta ^k$, or *copies of (oriented) $k$-dimensional [[ball]]s ${\bf B}^k$, or
  8 KB (1,367 words) - 13:49, 4 August 2013
• Social choice
  <!--150-->[[image:simplex of choices.png|center]] ...se.''' Generalize the conclusion of the last example to the case of an $n$-simplex.
  47 KB (8,030 words) - 18:48, 30 November 2015
• Orientation
  *an ''oriented'' interval: $[ a, b ] = -[ b, a ]$. ...ses]] of orderings of any set, in particular on the set of vertices of a [[simplex]], as follows:
  4 KB (753 words) - 03:35, 21 October 2012
• Higher order votes
  ...are ordered. We also suppose that these candidates are the vertices of an oriented simplicial complex $K$. All candidates are subject to evaluation but the pr <!--150-->[[image:simplex of choices.png| center]]
  41 KB (6,942 words) - 05:04, 22 June 2016