Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:172AE GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 10√2, 11√2, 18, 15√2, 25√2, 36, 29√2, 34√2, 50, 36√2, 52, 58, 44√2, 68, 70, 50√2, 52√2, 60√2, 68√2.

Code: 685 0 104 684 68 104 583 136 114 367 136 172 366 136 136 112 147 125 250 147 125 440 78 114 294 107 85 522 52 52 344 34 70 156 107 85 507 122 100 506 122 50 181 52 70 707 52 70 106 112 60 600 112 60 523 52 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)