<image>As shown in the figure, if a shape similar to the diagrams of a, b, c, and d is called a planar graph, then there exists a certain relationship between the number of vertices, edges, and regions. Observe Figure b and the corresponding values in the table to explore the counting method and answer the following questions. 
(1) Count the number of vertices, edges, and the regions formed by these edges in each graph, and fill in the table: \frac{}
(2) Based on the table values, write down a relationship between the number of vertices, edges, and regions in a planar graph;
(3) If a planar graph has 20 vertices and 11 regions, then using the relationship derived in (2), it can be determined that this planar graph has ______ edges.