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In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory.
A participle is a verbal that is used as an adjective and most often ends in-ing or-ed. The term verbal indicates that a participle, like the other two kinds of verbals, is based on a verb and therefore expresses action or a state of being. A participle is a verbal ending in-ing (present) or-ed, -en, -d, -t, -n, or-ne (past) that functions as an adjective, modifying a noun or pronoun. 2  A participial phrase consists of a participle plus modifier(s), object(s), and/or complement(s).