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Let Eaðu; vÞ be the extremal algebra determined by two hermitians u and v with u 2 ¼ v 2 ¼ 1. We show that: Eaðu; vÞ ¼ f f þ gu : f; g 2 CðTÞg, where T is the unit circle; Eaðu; vÞ is C Ã -equivalent to C Ã ðGÞ, where G is the infinite dihedral group; most of the hermitian elements k of Eaðu; vÞ have the property that k n is hermitian for all odd n but for no even n; any two hermitian words in G generate an isometric copy of Eaðu; vÞ in Eaðu; vÞ.doi:10.1017/s0017089502020062 fatcat:vrburupi7feztp2gezxsuswf34