Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:452AB GHM

Order: 20

Horizontal side: 452 Vertical side: 452

Elements: 12, 11√2, 12√2, 22, 24, 24√2, 36√2, 40√2, 80, 84, 102, 120, 102√2, 113√2, 168, 124√2, 204, 226, 248, 226√2.

Code: 2485 0 204 2264 226 226 2263 452 226 221 248 226 1025 248 124 1024 350 124 1136 339 113 2045 0 0 1681 168 204 1205 168 84 801 248 204 404 288 84 1240 328 124 114 339 113 242 192 60 241 192 84 122 204 72 121 204 84 847 204 84 366 168 36

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)