# Simplex

### From Glossary

(pl. *simplices*).
For , this is a point For n=2, this is a line segment, joining points (1,0) and (0,1). For this is a triangle, joining the vertices (1,0,0), (0,1,0), and (0,0,1). This is sometimes called an *n-simplex*, denoted by (note its dimension is n-1). The *open simplex* excludes the axes:

More generally, some authors define a simplex to be the convex hull of any affinely independent vectors, and refer to the special case of the unit vectors as the *standard simplex*.