Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:242AH GHM

Order: 20

Horizontal side: 242 Vertical side: 242

Elements: 12√2, 16√2, 24, 22√2, 32, 42, 44, 32√2, 48, 57, 44√2, 45√2, 64, 66, 81, 88, 64√2, 88√2, 97√2, 121√2.

Code: 1212 121 121 974 97 145 160 194 242 481 242 242 813 178 145 327 178 226 320 210 226 647 178 194 646 178 130 241 121 145 122 133 133 571 178 145 450 133 133 425 178 88 880 88 88 881 176 88 442 220 44 441 220 88 222 242 66 663 242 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)