Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AQ GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 16√2, 24, 18√2, 32, 24√2, 36, 40, 32√2, 48, 36√2, 37√2, 50√2, 74, 54√2, 98, 74√2, 122, 98√2, 148, 135√2.

Code: 1485 0 122 1354 135 135 986 172 172 376 135 135 985 172 74 1225 0 0 544 54 68 366 72 86 407 108 122 240 148 122 160 124 98 481 172 98 186 54 68 365 72 50 327 108 82 320 140 82 247 172 74 740 196 74 741 270 74 504 122 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)