Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256AJ GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 12, 12√2, 15√2, 24, 30, 36, 34√2, 36√2, 60, 68, 49√2, 79, 60√2, 68√2, 98, 109, 79√2, 90√2, 132, 98√2.

Code: 985 0 158 984 98 158 1323 196 124 607 196 256 606 196 196 362 232 160 363 232 124 245 232 136 792 79 79 494 49 109 125 232 124 124 244 124 686 188 68 150 64 124 904 154 34 301 79 109 1095 79 0 793 79 0 346 154 34 685 188 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)