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Introduction. Cannonballs and Tomatoes. The Puzzle of the Dozen Spheres. Parasols, Water Hydrants, and Soccer Players. Thue's Two Attempts and Fejes-Toth's Achievement. Twelve's Company, Thirteen's a Crowd. Nets and Knots. Twisted Boxes. No Dancing at this Congress. The Race for the Upper Bound. Right Angles for round Spaces. Wobbly Balls and Hybrid Stars. Simplex, Cplex, and Symbolic Mathematics. Bit Is It Really a Proof? Beehives Again... This Is Not An Epilogue. Mathematical Appendices. Bibliography. Index.