Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:140AS GHM

Order: 19

Horizontal side: 140 Vertical side: 140

Elements: 1√2, 2, 2√2, 4, 4√2, 8, 11√2, 19, 15√2, 22, 25, 22√2, 44, 48, 59, 70, 81, 59√2, 70√2.

Code: 815 0 59 704 70 70 703 140 70 114 81 59 10 92 70 481 140 70 20 91 69 21 93 69 255 93 44 83 89 59 42 93 63 41 93 67 193 93 44 597 0 59 590 59 59 154 74 44 441 118 44 222 140 22 223 140 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)