Primitive Perfect Isosceles Right Triangled Square

Title: d 20:264AA GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 27√2, 29√2, 32√2, 54, 58, 64, 75, 54√2, 81, 58√2, 61√2, 87, 90, 64√2, 93, 96, 102, 75√2, 81√2, 87√2.

Code: 1027 0 264 750 102 264 751 177 264 877 177 264 876 177 177 276 0 162 547 27 189 546 27 135 967 81 189 646 113 125 582 235 119 812 81 81 326 81 93 645 113 61 583 235 61 292 264 90 935 81 0 903 264 0 813 81 0 614 174 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)