From Square Tiling: “M. Laczkovich has shown that there are exactly three shapes of non-right triangles that tile the square with similar copies.” One of them is the 45°-60°-75° triangle. In the Laczkovich paper, the proof outlined thousands of triangles with no picture. Tom Sirgedas got it down to 32 triangles, which is believed minimal.
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CITE THIS NOTEBOOK

The Tom Sirgedas 45°-60°-75° square dissection​
by Ed Pegg​
Wolfram Community, STAFF PICKS, March 4, 2025
​https://community.wolfram.com/groups/-/m/t/3408096