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Icosahedral Sets in PG(5, 2)

✍ Scribed by Ron Shaw

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 487 KB
Volume: 18
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0100

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✦ Synopsis

Starting out from the 15 pairs of opposite edges and the 20 faces of a coloured icosahedron , a simple new construction is given of a 'double-five' of planes in PG (5 , 2) . This last is a recently discovered configuration consisting of a set of (15 ϩ 20 ϭ )35 points in PG (5 , 2) which admits

five mutually skew planes . Moreover , r ϭ ␣ r ʝ ␤ r is a line , for each r , while n r s ϭ ␣ r ʝ ␤ s is a point , for r ϶ s . The new construction illuminates why the symmetry group of is isomorphic to A 5 ϫ Z 2 . The set is a set of hyperbolic type , and it has a cubic equation .

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