Illumination of Pascal’s Hexagrammum and Octagrammum Mysticum

We prove general results which include classical facts about the 60 lines of Pascal as special cases. Along similar lines we establish analogous results about the configurations of 2,520 conics arising from the mystic octagon. We offer a more combinatorial outlook on these results. Bézout’s theorem is the main tool; however, its application is guided by the empirical evidence and computer experiments with the program Cinderella .