The convex hull of any nonempty subset of the points that define an -simplex is called a face of the simplex. Faces are simplices themselves. In particular, the convex hull of a subset of size (of the defining points) is an -simplex, called an -face of the -simplex. The 0-faces (i.e., the defining points themselves as sets of size 1) are called the vertices (singular: vertex), the 1-faces are called the edges, the ()-faces are called the facets, and the sole -face is the whole -simplex itself. In general, the number of -faces is equal to the binomial coefficient . Consequently, the number of -faces of an -simplex may be found in column () of row () of Pascal's triangle. A simplex is a coface of a simplex if is a face of . Face and facet can have different meanings when describing types of simplices in a simplicial complex.
The convex hull of any nonempty subset of the points that define an -simplex is called a face of the simplex. Faces are simplices themselves. In particular, the convex hull of a subset of size (of the defining points) is an -simplex, called an -face of the -simplex. The 0-faces (i.e., the defining points themselves as sets of size 1) are called the vertices (singular: vertex), the 1-faces are called the edges, the ()-faces ar:e called the facets, and the sole -face is the whole -simplex itself. In general, the number of -faces is equal to the binomial coefficient . Consequently, the number of -faces of an -simplex may be found in column () of row () of Pascal's triangle. A simplex is a coface of a simplex if is a face of . Face and facet can have different meanings when describing types of simplices in a simplicial complex.