Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AA GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 20√2, 26√2, 28√2, 52, 37√2, 56, 62, 46√2, 72, 74, 56√2, 57√2, 62√2, 94, 102, 74√2, 114, 84√2, 124, 104√2.

Code: 1042 104 166 844 84 186 280 168 270 1021 270 270 560 140 242 561 196 242 742 270 168 204 104 166 1243 124 62 727 124 186 466 150 140 743 270 94 260 150 140 527 124 114 1143 176 0 572 233 57 374 233 57 943 270 0 625 0 0 624 62 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)