Regular 4-polytopes from the Livingstone graph of Janko’s first group

The Janko group J 1 has, up to duality, exactly two regular rank four polytopes, of respective Schläfli types {5,3,5} and {5,6,5}. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of algebraic combinatorics 2012-03, Vol.35 (2), p.193-214
Hauptverfasser:	Hartley, Michael I., Hubard, Isabel, Leemans, Dimitri
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures
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Beschreibung
Zusammenfassung:	The Janko group J 1 has, up to duality, exactly two regular rank four polytopes, of respective Schläfli types {5,3,5} and {5,6,5}. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.
ISSN:	0925-9899 1572-9192
DOI:	10.1007/s10801-011-0300-x