Sentence:  A <WSD>"triangulation</WSD>" of a point configuration \mathbf{A} \in \mathbb{R}^d is a collection  of "d"-simplices all of whose vertices are points in \mathbf{A} that satisfies the following two properties: 1.  The union of all these simplices equals conv(\mathbf{A}). ("Union Property") 2. Any pair of these simplices intersects in a common face (possibly empty). ("Intersection Property") 
Meaning of the word marked with <WSD> tags:  A subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.