Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:456AA2of2 GHM

Order: 20

Horizontal side: 456 Vertical side: 456

Elements: 22√2, 32, 24√2, 44, 32√2, 48, 64, 48√2, 88, 64√2, 66√2, 72√2, 81√2, 88√2, 162, 125√2, 206, 250, 184√2, 228√2.

Code: 2505 0 206 2284 228 228 1846 272 272 443 272 228 722 344 200 224 250 206 666 206 162 2065 0 0 1254 125 81 240 344 200 480 320 176 481 368 176 882 456 88 816 125 81 1625 206 0 327 272 128 326 272 96 647 304 128 646 304 64 883 456 0

The properties below may precede order:side in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
• d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
• i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
• r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.

Credit for Discovery

Just three people are credited with the discovery of Primitive Perfects:

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)

William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)