Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AQ GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 15√2, 17√2, 30, 24√2, 34, 40, 48, 34√2, 64, 66, 48√2, 51√2, 64√2, 66√2, 72√2, 102, 104, 102√2, 104√2, 119√2.

Code: 1192 119 153 1044 104 168 1043 208 168 647 208 272 646 208 208 405 208 168 154 119 153 660 134 168 661 200 168 482 248 120 481 248 168 242 272 144 726 200 72 516 17 51 1027 68 102 1020 170 102 301 200 102 170 17 51 347 0 34 340 34 34

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)