Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:269AA GHM

Order: 20

Horizontal side: 269 Vertical side: 269

Elements: 4, 14, 14√2, 28, 21√2, 42, 49, 53, 42√2, 51√2, 53√2, 55√2, 98, 102, 106, 108, 110, 112, 108√2, 110√2.

Code: 1105 0 159 1104 110 159 210 220 269 491 269 269 420 199 248 421 241 248 285 241 220 145 241 206 144 255 206 1123 269 108 1023 157 104 987 157 206 1065 0 53 554 55 104 47 157 108 1080 161 108 1081 269 108 514 106 53 535 0 0 534 53 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)