Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:225AB GHM

Order: 20

Horizontal side: 225 Vertical side: 225

Elements: 14, 18√2, 27, 33, 36, 27√2, 47, 36√2, 53, 54, 40√2, 66, 47√2, 72, 53√2, 66√2, 72√2, 106, 86√2, 132.

Code: 862 86 139 724 72 153 723 144 153 362 180 189 541 198 225 272 225 198 271 225 225 1323 225 66 363 180 153 182 198 171 141 86 153 475 86 106 474 133 106 333 86 106 536 0 53 1065 53 0 404 93 66 664 159 0 663 225 0 535 0 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)