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COORDINATES FOR THE REGULAR COMPLEX POLYGONS

Published online by Cambridge University Press:  01 June 1997

H. S. M. COXETER ,
J. CHRIS FISHER  and
J. B. WILKER
H. S. M. COXETER
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3
J. CHRIS FISHER
Affiliation:
Department of Mathematics, University of Regina, Regina, Canada S4S O2A
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Abstract

Certain projections of the real polytopes {3, 3, 4}, {3, 4, 3}, {3, 3, 5} suggest highly symmetric coordinates for the self-reciprocal complex polygons 3{3}3, 4{3}4, 3{4}3, 5{3}5 and 3{5}3. Although there are a number of interesting complications, this suggestion is essentially correct and leads to elegant coordinates for all the sporadic complex polygons. Among the by-products of producing these coordinates we count most significant our new insights about 2{6}3 and our simple proof that the 600 vertices of the real polytope {5, 3, 3} are quite unrelated to the 600 vertices of either 5{6}2 or 5{4}3.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 527 - 548
Copyright
The London Mathematical Society 1997

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