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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

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