Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:242AS GHM

Order: 20

Horizontal side: 242 Vertical side: 242

Elements: 6√2, 17√2, 19√2, 22√2, 28√2, 34√2, 36√2, 56, 68, 50√2, 72, 51√2, 53√2, 68√2, 70√2, 100, 72√2, 102, 106, 136.

Code: 1367 0 242 1003 136 142 502 186 192 1061 242 242 286 158 164 565 186 136 220 158 164 366 0 106 725 36 70 724 108 70 60 180 142 346 140 102 687 174 136 686 174 68 532 53 53 516 89 51 1025 140 0 174 53 53 700 70 70 194 89 51

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)