Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:147AB GHM

Order: 20

Horizontal side: 147 Vertical side: 147

Elements: 4, 24, 18√2, 28, 21√2, 32, 24√2, 36, 29√2, 42, 32√2, 47, 48, 36√2, 52, 37√2, 58, 42√2, 63, 63√2.

Code: 637 0 147 636 0 84 527 63 147 283 115 119 327 115 147 326 115 115 240 87 119 241 111 119 362 147 83 41 115 119 372 100 58 481 111 95 422 42 42 363 147 47 583 100 0 292 129 29 184 129 29 473 147 0 423 42 0 212 63 21

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)