Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:236AW GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 2, 15√2, 17√2, 22√2, 34, 36, 26√2, 44, 34√2, 36√2, 52, 52√2, 74, 88, 96, 70√2, 74√2, 140, 118√2.

Code: 1405 0 96 1184 118 118 746 162 162 443 162 118 745 162 88 224 140 96 156 147 103 170 147 103 965 0 0 704 70 26 21 164 88 365 164 52 364 200 52 883 236 0 340 130 86 341 164 86 266 70 26 525 96 0 524 148 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)