We enumerate all dissections of an equilateral triangle into smaller
equilateral triangles up to size 20, where each triangle has integer side
lengths. A perfect dissection has no two triangles of the same side, counting
up- and down-oriented triangles as different. We computationally prove W. T.
Tutte's conjecture that the smallest perfect dissection has size 15 and we find
all perfect dissections up to size 20.Comment: Final version sent to journal