Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:172AR4of4 GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 3√2, 6, 6√2, 12, 9√2, 13, 18, 13√2, 21, 26, 34, 26√2, 52, 60, 73, 86, 99, 73√2, 86√2.

Code: 995 0 73 864 86 86 863 172 86 134 99 73 133 112 73 345 112 52 601 172 86 737 0 73 730 73 73 181 91 73 125 91 61 211 112 73 65 91 55 64 97 55 90 103 61 34 94 52 521 146 52 262 172 26 263 172 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)