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I have been trying to hunt down the original reference for the construction of the projective plane of order $4$ from the complete graph on $6$ vertices.

The reference I have at hand are Cameron and van Lint (Chapter 6) and Beutelspacher.

Cameron and van Lint vaguely credit lecture notes by G. Higman, and I'm finding some of Beutelspacher's references hard to access. Does anyone know offhand where this first appeared? Any help will be greatly appreciated.

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All references converge on W.L. Edge, Some implications of the geometry of the 21-point plane, Math.Zeitschr. 87, 348--362 (1965) Available at http://www.maths.ed.ac.uk/cheltsov/edge2013/pdf/1965a.pdf

Section 6 lays out all the necessary ideas.

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Maybe this book http://www.google.com/search?tbo=p&tbm=bks&q=isbn:3540617868 (Peter Dembowski, Finite Geometries) can help. It has extensive bibliography. Was reprinted in 1997: http://www.amazon.com/Finite-Geometries-Classics-Mathematics-Dembowski/dp/3540617868

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