Determine the resistance \( R_{A B} \) between points \( A \) and \...

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Determine the resistance \( R_{A B} \) between points \( A \) and \( B \) of the frame made of thin homogeneous wire (as shown in figure), assuming that the number of successively embedded equilateral triangles (with sides decreasing by half) tends to infinity. Side \( A B \) is equal to \( a \), and the resistance of unit length of the wire is \( \rho \).
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