Vol. 1, No. 1, 2005

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On the thin regular geometries of rank four for the Janko group $J_1$

Michael Hartley and Dimitri Leemans

Vol. 1 (2005), No. 1, 181–190

The Janko group J1 acts regularly on six rank four thin residually connected geometries. Two of them are polytopes of type {5,3,5} and {5,6,5}. In this paper, we show that starting from the {5,3,5} polytope, the five other thin geometries may be constructed in a simple manner.

abstract polytopes, thin geometries, sporadic group
Mathematical Subject Classification 2000
Primary: 20F65, 51M20, 52B15
Received: 1 October 2004
Accepted: 2 December 2004
Michael Hartley
Dimitri Leemans