Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:185AC GHM

Order: 20

Horizontal side: 185 Vertical side: 185

Elements: 8, 8√2, 14√2, 28, 33, 24√2, 43, 32√2, 33√2, 48, 56, 43√2, 66, 48√2, 71, 72, 80, 81, 86, 71√2.

Code: 817 0 185 480 81 185 481 129 185 242 153 161 561 185 185 320 153 161 336 0 104 665 33 71 801 113 137 85 113 129 84 121 129 727 113 129 863 185 43 335 0 71 717 0 71 710 71 71 281 99 71 142 113 57 434 142 0 433 185 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)