Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AZ GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 15, 20, 15√2, 20√2, 21√2, 30, 40, 42, 30√2, 32√2, 63, 45√2, 64, 84, 64√2, 74√2, 106, 85√2, 148, 127√2.

Code: 1485 0 106 1274 127 127 856 169 169 423 169 127 452 214 124 214 148 106 633 169 64 306 184 94 405 214 84 1065 0 0 744 74 32 156 169 79 305 184 64 205 214 64 204 234 64 843 254 0 155 169 64 326 74 32 645 106 0 644 170 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)