Explore a fascinating seminar on advanced geometry, delving into five-fold symmetry, Schiffler points, and the twisted icosahedron. Discover the interplay between projective and triangle geometry, examining dihedral orderings and a unique distance-regular graph. Investigate 12 remarkable conics arising from 5 points in the plane, with a focus on the Schiffler point (triangle center X_21 in Kimberling's list). Learn about the Emelyanov brothers' interpretation and its broad generalization. Journey through topics including quadrangle-quadrilateral duality, Pascal's theorem, and dihedral conics, gaining deep insights into this intriguing area of mathematics.