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Area definition at a vertex. For the vertex at the center (cyan), the area is defined as the total area of the region shown in magenta, which is made up of all the triangles constructed by connecting the vertex (cyan), the centroid (black) of its neighboring triangle and the middle point (yellow) of its neighboring ring in the same triangle. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
