Journal for Geometry and Graphics 24 (2020), No. 2, 175--191
Copyright Heldermann Verlag 2020
The Pentagrammum Mysticum, Twelve Special Conics and the Twisted Icosahedron
Nguyen Le
Dept. of Mathematics, San Francisco State University, U.S.A.
nguyenlecm2009@gmail.com
Norman J. Wildberger
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
n.wildberger@unsw.edu.au
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.
Keywords: Strongly regular graph, icosahedron, Pascal theorem, conic, pentagon.
MSC: 14Nxx; 51A20, 05Exx
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