Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:124AV GHM

Order: 19

Horizontal side: 124 Vertical side: 124

Elements: 11, 9√2, 14, 17, 17√2, 28, 33, 24√2, 34, 38, 39, 28√2, 33√2, 48, 34√2, 52, 38√2, 43√2, 48√2.

Code: 485 0 76 484 48 76 393 96 85 287 96 124 286 96 96 115 96 85 330 57 85 331 90 85 177 90 85 170 107 85 382 38 38 244 24 52 347 90 68 346 90 34 141 38 52 527 38 52 96 81 43 430 81 43 383 38 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)