Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:264AC1of8 GHM

Order: 19

Horizontal side: 264 Vertical side: 264

Elements: 8√2, 10√2, 16, 20, 16√2, 32, 24√2, 40, 30√2, 32√2, 40√2, 51√2, 80, 71√2, 102, 122, 142, 112√2, 132√2.

Code: 1425 0 122 1324 132 132 1126 152 152 203 152 132 242 176 128 104 142 122 306 122 102 80 176 128 1225 0 0 714 71 51 160 168 120 161 184 120 805 184 40 327 152 104 326 152 72 516 71 51 1025 122 0 404 224 0 403 264 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)