Consider regular polygons with number of sides $n=3,4,5 \ldots \ldots$ as shown in the figure, The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted,. The maximum increase in height of the locus of the center of mass for each polygton is $\Delta$. Then $\Delta$ depends on $n$ and $h$ as