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Fundamental figures, in four and six dimensions, over GF(2)

Published online by Cambridge University Press:  24 October 2008

W. L. Edge
W. L. Edge
Affiliation:
University of Edinburgh
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Extract

Introduction. This paper falls into three parts.

In §§ 1–5 it is explained how, when the base field of the geometry is GF(2), there are figures of n + 2 interlocking polygons in [n], every two polygons sharing a vertex. When n is even these ½(n + 1) (n + 2) vertices lie in an [n − 1], and two of them are conjugate in a certain null polarity when, and only when, they do not belong to the same polygon.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 2 , April 1964 , pp. 183 - 195
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Burnside, W.On the double six which admits a group of 120 collineations into itself. Proc. Cambridge Philos. Soc. 16 (1911), 418–420.Google Scholar
(2)Coble, A. B.A generalisation of the Weddle surface, of its Cremona group, and of its parametric expression in terms of hyperelliptic theta functions. American J. Math. 52 (1930), 439–500.Google Scholar
(3)Conwell, G. M.The 3-space PG(3, 2) and its group. Ann. of Math. (2) 11 (1910), 60–76.Google Scholar
(4)Edge, W. L.The geometry of the linear fractional group LF (4, 2). Proc. London Math. Soc. (3) 4 (1954), 317–342.Google Scholar
(5)Edge, W. L.Quadrics over GF(2) and their relevance for the cubic surface group. Canadian J. Math. 11 (1959), 625–645.Google Scholar
(6)Hudson, R. W. H. T.Kummer's quartic surface (Cambridge, 1905).Google Scholar
(7)Richmond, H. W.The figure formed from six points in space of four dimensions. Math. Ann. 53 (1900), 161–176.Google Scholar
(8)Richmond, H. W.The figure formed from six points in space of four dimensions. Quart. J. Pure Appl. Maths. (1899), 125–160.Google Scholar
(9)Room, T. G.A generalization of the Kummer 166 configuration (I). Proc. London Math. Soc. (2) 37 (1934), 292–337.Google Scholar
(10)Sylvester, J. J.Elementary researches in the analysis of combinatorial aggregation. Phil Mag. 24 (1844), 285–296 (reprinted in Mathematical Papers, 1, 91–102).Google Scholar