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We study the martingale isoperimetric profile \\[ V_n(x):= \\inf_{\\substack{A\\subset[0,1)\\ {\\rm measurable}\\\\ |A|=x}} \\|S_1(\\mathbbm 1_A)\\|_1 . \\] For the ternary filtration we determine this profile exactly. Namely, \\[ V_3(x)=T_3(x):= \\sum_{j=0}^{\\infty}3^{-j}\\psi_3(\\{3^j x\\}), \\] where \\[ \\psi_3(t)= \\min\\left\\{ \\frac{1+2\\left|t-\\frac12\\right|}{3}, \\frac{2-4\\left|t-\\frac12\\right|}{3} \\right\\}, \\qquad 0\\le t\\le1 . \\] Thus the sharp ternary profile is a Takagi-type Bellman function. 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