Geodesic
The Pentagrammum Mysticum, Twelve Special Conics and the Twisted Icosahedron
Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 175-191
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We study an abstract pentagon in planar projective geometry via its unique circumscribing conic, associated to 15 diagonal lines and exagonal points, and describe 12 beautifully inter-related conics. These are closely connected to a distance-regular graph X which is a sister of the icosahedral graph, arising from dihedral orderings of five objects.
Classification : 14Nxx, 51A20, 05Exx
Mots-clés : Strongly regular graph, icosahedron, Pascal theorem, conic, pentagon 
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     author = {N. Le and N. J. Wildberger},
     title = {The {Pentagrammum} {Mysticum,} {Twelve} {Special} {Conics} and the {Twisted} {Icosahedron}},
     journal = {Journal for geometry and graphics},
     pages = {175--191},
     year = {2020},
     volume = {24},
     number = {2},
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N. Le; N. J. Wildberger. The Pentagrammum Mysticum, Twelve Special Conics and the Twisted Icosahedron. Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 175-191. http://geodesic.mathdoc.fr/item/JGG_2020_24_2_JGG_2020_24_2_a2/