Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AY GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 8√2, 16, 16√2, 18√2, 24√2, 26√2, 48, 35√2, 52, 40√2, 44√2, 48√2, 70, 88, 96, 79√2, 114, 88√2, 158, 136√2.

Code: 1585 0 114 1364 136 136 963 272 176 406 136 136 485 176 128 484 224 128 886 184 88 162 192 112 244 200 104 1145 0 0 794 79 35 180 158 114 163 192 96 82 200 104 266 114 70 527 140 96 446 140 44 885 184 0 356 79 35 705 114 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)