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Journal of the London Mathematical Society 1997 55(3):527-548; doi:10.1112/S0024610797004936
© 1997 by London Mathematical Society
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© The London Mathematical Society

Coordinates for the Regular Complex Polygons

H. S. M. Coxeter, J. Chris Fisher and J. B. Wilker

Department of Mathematics, University of Toronto Toronto, Canada M5S 3G3
Department of Mathematics, University of Regina Regina, Canada S4S O2A

Received 12 January 1995.

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.


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