Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:296AC2of2 GHM

Order: 20

Horizontal side: 296 Vertical side: 296

Elements: 8, 8√2, 16, 16√2, 28, 32, 28√2, 32√2, 37√2, 46√2, 51√2, 74, 56√2, 102, 74√2, 120, 97√2, 148, 111√2, 148√2.

Code: 1485 0 148 1484 148 148 976 199 199 510 199 199 742 74 74 1114 111 37 280 222 148 281 250 148 462 296 102 1203 194 0 87 194 120 86 194 112 167 202 120 166 202 104 327 218 120 326 218 88 562 250 56 1023 296 0 743 74 0 372 111 37

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)