$N$ regular polygons with $E$ edges each meet at a point with no intervening space. Show that $N = \frac{2E}{E-2}\qquad E=\frac{2N}{N-2}$ I did this part considering that the internal angles must add up to $2\pi$ , i.e $\left( 1 -\dfrac2E \right)\pi\times N =2\pi $. I am unable to explain the following:
Using the result given above, show that the only possibilities are $E=3,4,6$