Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:292AJ GHM

Order: 20

Horizontal side: 292 Vertical side: 292

Elements: 2, 2√2, 4, 4√2, 28√2, 42, 31√2, 48, 56, 42√2, 62, 56√2, 84, 62√2, 90, 118, 87√2, 146, 174, 146√2.

Code: 1745 0 118 1464 146 146 1463 292 146 284 174 118 843 202 62 422 244 104 901 292 146 1185 0 0 874 87 31 423 244 62 485 244 56 316 87 31 625 118 0 624 180 0 20 242 62 21 244 62 40 240 60 41 244 60 560 236 56 561 292 56

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)