The Veronese Surface in PG(5, 3) and Witt's 5-(12, 6, 1) Design

A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, 6, 1) design, the blocks being the hyperplane sections containing more than three (actually six) points of K. As such a point model is projectively unique, the present construction yields an easy coordinate–free approach to some results obtained independently by H.S.M. Coxeter and G. Pellegrino, including a projective representation of the Mathieu group M12 in PG(5, 3). ∗ Research supported by the Austrian FWF, project P12353–MAT. 1 

• Type: Journal
• Year: 1998
• Where: JCT
• Authors: Hans Havlicek
• Keywords: Easy Coordinate–free Approach, JCT 1998, Point Model, Veronese Surface