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Any progress on the following: Can a closed disc in the plane be partitioned into three disjoint sets which are pair-wise isometric, i.e. each set is an image of the others an isometry?

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Perhaps by "plane" he means the Euclidean plane, with Euclidean metric. – Joseph O'Rourke Jan 26 '13 at 14:52
    
@Joseph, thank you, I see "closed disc" and read "closed geodesic" --- I am getting older. – Anton Petrunin Jan 26 '13 at 17:56
    
Is it a well known problem? Any references? – Anton Petrunin Jan 26 '13 at 17:57

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