Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256AC GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 9, 9√2, 18, 18√2, 22√2, 42, 44, 43√2, 44√2, 48√2, 57√2, 84, 85, 86, 66√2, 84√2, 85√2, 86√2, 127, 129.

Code: 865 0 170 864 86 170 1293 172 127 847 172 256 846 172 172 182 190 154 852 85 85 434 43 127 183 190 136 662 256 88 95 172 127 94 181 127 576 133 79 421 85 127 1275 85 0 484 133 79 446 212 44 853 85 0 226 190 22 445 212 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)