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We study real solutions of a class of Painleve VI equations. To each suchsolution we associate a geometric object, a one-parametric family of circularpentagons. We describe an algorithm which permits to compute the numbers ofzeros, poles, 1-points and fixed points of the solution on the interval x>1 andtheir mutual position. The monodromy of the associated linear equation andparameters of the Painleve VI equation are easily recovered from the family ofpentagons.

Circular pentagons and real solutions of Painleve VI equations