# nLab barycenter

## Barycenter of a simplex

###### Definition

If $\sigma = \{ v_0, \ldots, v_q\} \in K_q$, the set of $q$-simplices of a simplicial complex, $K$, then its barycentre, $b(\sigma)$, is the point

$b(\sigma) = \sum_{0\leq i \leq q}\frac{1}{q + 1} v_i \in |K|.$

For the use of barycenters in the barycentric subdivision, see classical triangulation or

Revised on December 1, 2010 21:00:49 by Tim Porter (95.147.238.157)