Primitive Perfect Isosceles Right Triangled Square

Title: dr 19:198AC2of4 GHM

Order: 19

Horizontal side: 198 Vertical side: 198

Elements: 8, 7√2, 8√2, 14, 16, 12√2, 14√2, 24, 28, 21√2, 24√2, 28√2, 56, 71, 85, 99, 113, 85√2, 99√2.

Code: 1135 0 85 994 99 99 993 198 99 144 113 85 143 127 85 72 134 92 711 198 99 163 134 76 82 142 84 857 0 85 850 85 85 214 106 64 83 142 76 565 142 28 126 106 64 247 118 76 246 118 52 284 170 0 283 198 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)