A R Rao is at the Indian Statistical Institute, Calcutta..

This article is in two parts. In this first part, we will prove that a football exists and is unique and in the second, we identify its group of symmetries. (We will incidentally do similar things for the platonic solids to some of which the football is closely related.) I heard of this problem from Amit Roy of TIFR, Mumbai. The ideas used in the proof of the existence and uniqueness are also his. Most of the other proofs presented here can be found in Gallian (1999) and Coxeter (1948).

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Address for Correspondence
A R Rao
Indian Statistical Institute
203, B T Road
Calcutta 700 035, India.