Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:253AB GHM

Order: 20

Horizontal side: 253 Vertical side: 253

Elements: 13, 13√2, 26, 22√2, 39, 44, 55, 39√2, 65, 76, 55√2, 78, 88, 89, 99, 100, 76√2, 110, 88√2, 99√2.

Code: 995 0 154 994 99 154 550 198 253 551 253 253 443 143 154 222 165 176 1101 253 198 1003 165 76 882 253 88 657 0 154 396 26 115 787 65 154 263 26 89 395 26 76 895 0 0 134 13 76 133 26 76 883 253 0 764 89 0 763 165 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)