6. Color each vertex of a regular quadrilateral pyramid with one color, and make sure that the two ends of the same edge are different colors. Now, there are 5 colors available. The total number of different coloring schemes is $\qquad$ (it is agreed that coloring schemes that can be transformed into each other by rotating around the symmetry axis of the quadrilateral pyramid are considered the same coloring scheme).
6. 120. If all 5 colors are used, then choosing 1 color from 5 to dye the top vertex has $C_{5}^1$ methods, and the remaining 4 colors to dye the 4 vertices on the bottom (which should be a circular permutation of 4 elements) have $(4-1)!=6$ methods. In this case, the number of coloring schemes is $C_{5}^1 \times 6 = 30$. If only 4 colors are used, then choosing 4 colors from 5, and then choosing 1 color from the selected 4 to dye the top vertex has $C_{5}^4 C_{4}^1$ methods. The remaining 3 colors to dye the 4 vertices on the bottom (where one pair of vertices must be the same color) has $C_{3}^1$ methods to choose 1 color for the pair, and the remaining 2 colors to dye the remaining 2 vertices have $(2-1)!=1$ method. In this case, the number of coloring schemes is $C_{5}^4 C_{4}^1 C_{3}^1 \cdot 1 = 60$. If only 3 colors are used, then choosing 3 colors from 5 has $C_{5}^3$ methods, and choosing 1 color from the selected 3 to dye the top vertex has $C_{3}^1$ methods. The remaining 2 colors to dye the 4 vertices on the bottom (where 2 pairs of vertices must be the same color) have $(2-1)!=1$ method. In this case, the number of coloring schemes is $C_{5}^3 \cdot C_{3}^1 = 30$. Therefore, the total number of different coloring schemes is $30 + 60 + 30 = 120$.