Pure partial planes of order 6 with 25 lines

Authors:
Alan R. Prince
Affiliations:
Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland EH14 4AS
Venue:
Designs, Codes and Cryptography
Year:
2009

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Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
A partial plane of order 6 constructed from the icosahedron

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Abstract

We construct two pure partial planes of order 6 with 25 lines, which extend the dual of the linear space PG(3,2). One of these is of particular interest since its dual is a pseudo-complement of a triangle in a projective plane of order 6.