Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:162AY4of8 GHM

Order: 19

Horizontal side: 162 Vertical side: 162

Elements: 1√2, 2, 2√2, 4, 4√2, 8, 7√2, 14, 15√2, 22√2, 37, 44, 37√2, 59, 44√2, 81, 59√2, 103, 81√2.

Code: 1035 0 59 814 81 81 813 162 81 224 103 59 370 125 81 371 162 81 597 0 59 590 59 59 141 73 59 85 73 51 154 88 44 45 73 47 44 77 47 70 81 51 25 73 45 24 75 45 14 74 44 444 118 0 443 162 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)