Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:167AA4of4 GHM

Order: 20

Horizontal side: 167 Vertical side: 167

Elements: 2, 2√2, 4, 9√2, 18, 18√2, 36, 27√2, 41, 43, 36√2, 40√2, 41√2, 42√2, 43√2, 45√2, 81, 83, 84, 86.

Code: 865 0 81 841 84 167 422 126 125 831 167 167 406 86 85 412 167 84 26 84 83 45 86 81 413 167 43 815 0 0 364 36 45 363 72 45 182 90 63 181 90 81 92 99 72 270 99 72 454 81 0 23 126 43 430 124 43 431 167 43

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)