Geodesic
The Pentagrammum Mysticum, Twelve Special Conics and the Twisted Icosahedron
Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 175-191.

Voir la notice de l'article provenant de la source Heldermann Verlag

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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     title = {The {Pentagrammum} {Mysticum,} {Twelve} {Special} {Conics} and the {Twisted} {Icosahedron}},
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     pages = {175--191},
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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/