Schoute (1910) showed that the 27 lines can be put into a one-to-one correspondence with the vertices of a particular polytope
in six-dimensional space in such a manner that all incidence relations between the
lines are mirrored in the connectivity of the polytope
and conversely (Du Val 1933). A similar correspondence can be made between the 28
bitangents and a seven-dimensional polytope (Coxeter
1928) and between the tritangent planes of the canonical curve of genus four and
an eight-dimensional polytope (Du Val 1933).
Bell, E. T. The Development of Mathematics, 2nd ed. New York: McGraw-Hill, pp. 322-325,
1945.Coxeter, H. S. M. "The Pure Archimedean Polytopes
in Six and Seven Dimensions." Proc. Cambridge Phil. Soc.24, 7-9,
1928.Du Val, P. "On the Directrices of a Set of Points in a Plane."
Proc. London Math. Soc. Ser. 235, 23-74, 1933.Schoute,
P. H. "On the Relation Between the Vertices of a Definite Sixdimensional
Polytope and the Lines of a Cubic Surface." Proc. Roy. Akad. Acad. Amsterdam13,
375-383, 1910.
