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Polytopes Over GF(2) and their Relevance for the Cubic Surface Group

Published online by Cambridge University Press:  20 November 2018

H. S. M. Coxeter
H. S. M. Coxeter*
Affiliation:
University of Toronto
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In the preceding paper, Edge represented the celebrated “cubic surface group” of order 72.6! = 51840 as the group of automorphisms of a senary quadratic form over the field of residue-classes mod 2. The object of this sequel is to compare Edge's finite space with a real space, thus identifying his non-ruled quadric in PG(5, 2) with a modular counterpart of the semi-regular polytope 221 which was discovered by Gosset in 1897.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 646 - 650
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Coxeter, H. S. M., The polytopes with regular-prismatic vertex figures, Philos. Trans. Roy. Soc. London, Ser. A, 229 (1930), 329–425.Google Scholar
2. Coxeter, H. S. M., Finite groups generated by reflections and their subgroups generated by reflections, Proc. Cambridge Philos. Soc, 80 (1934), 466-82.Google Scholar
3. H. S. M. Coxeter, , The poly tope 22i whose 27 vertices correspond to the lines on the general cubic surface, Amer. J. Math., 62 (1940), 457-86.Google Scholar
4. Coxeter, H. S. M., Regular polytopes (London, 1948).Google Scholar
5. Coxeter, H. S. M., Extreme forms, Can. J. Math., 3 (1951), 391–441.Google Scholar
6. Edge, W. L., Quadrics over GF(2) and their relevance for the cubic surface group, Can. J. Math 11 (1959), 631-51.Google Scholar