Vertex centroid ($c=\frac{1}{n}{\sum }_{j=0}^{n-1}{v}_j$)

The arithmetic mean of a finite nonempty collection of vertices, treating each vertex as an equal point mass. For a polygon, this need not equal the uniform-area centroid of its interior. A translation or linear map commutes with this average; consequently rotating all vertices about their vertex centroid leaves that centroid fixed.