We use Divide and Conquer (D&C) method to solve two Diophantine equations and show how to obtain all vertex sets of deltahedra. Having solved the problem by manually employed this method, we validated all of the solutions for n=4,6,…,22, with the results of the computer programming of the same algorithm. We then verify the integrity of the solutions by backtracking and nested loop search methods. The iterations of the two search methods obviously are multiply times of the same as the D&C method for n=4,6,…,100. Finally, we employed the D&C method to solve the problem and found the ratios of consecutive solutions for n=4,6,…,300 asymptotically approach to unity.
