Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:172AW GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 9, 16, 12√2, 16√2, 24, 18√2, 21√2, 32, 33, 24√2, 36, 26√2, 42, 44, 65, 86, 65√2, 107, 86√2.

Code: 1075 0 65 864 86 86 863 172 86 214 107 65 180 128 86 441 172 86 120 110 68 361 146 68 262 172 42 657 0 65 650 65 65 331 98 65 97 98 65 247 98 56 240 122 56 423 172 0 321 130 32 162 146 16 161 146 32

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)