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Special cases of rectangles, where the root of the ratio of sides is a rational number, so that there are rotational angles where the vertices line up along the axes again.

The square series: 1x1, 2x1, 3x1, 4x1, 5x1, 3x2, 4x3

The A-paper (root 2) series: 1x1, 2x1, 3x1

The triad (root 3) series: 1x1, 2x1, 2x1 (lengthwise), 4x1

Also the root-fivers: √3 by √2 and 2 by 1
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rotated rectangle root 1:4:5 rotated rectangle root 9:16:25 rotated rectangle root 1:3:4 rotated rectangle root 1:4:5 sq rotated rectangle root 1:1:2 rotated rectangle root 2:3:5 rotated rectangle root 3:16:19 rotated rectangle root 2:9:11 rotated rectangle root 1:2:3 rotated rectangle root 1:8:9 rotated rectangle root 1:25:26 rotated rectangle root 1:16:17 sq rotated rectangle root 4:9:13 rotated rectangle root 1:12:13 rotated rectangle root 1:9:10 sq rotated rectangle root 3:4:7