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What is the smallest number of strictly isosceles acute triangles that an equilateral triangle can be divided into? The following construction is by WR Somsky, with 13 triangles. Is this minimal? enter image description here

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I take it "strictly isosceles" means no equilateral triangles allowed, and "acute" means no right triangles allowed. –  Gerry Myerson Jun 21 '12 at 1:28
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WR Somsky is totally dominating this question. He's lowered it to 12 triangles. Since every 60 degree angle needs to be split, this is likely approaching a level where a minimality proof exists. 12 triangle construction

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