Forum Geometricorum, 8 (2008) 175--182.

Abstract: Suppose a,b,c are algebraic indeterminates. The mapping (a,b,c) -> (bc,ca,ab) is an example of a second-degree involutory symbolic substitution (SISS) which maps the transfigured plane of a triangle to itself. The main result is a classification of SISSs as four individual mappings and two families of mappings. The SISS (a,b,c)->(bc,ca,ab) maps the circumcircle onto the Steiner ellipse. This and other examples are considered.

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