What software would allow me to render points, vertices and faces within shapes?

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I am trying to solve this problem https://www.youtube.com/watch?v=84hEmGHw3J8 (please do not tell me the solution!) and think I have to find out the number of points, edges and faces for each increase in points on the circumference of the circle.

I am not capable of drawing these though, as the numbers of each are getting to over a hundred - is there any software I can use to help me with complex geometric drawings like these?