Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AV GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 15√2, 24, 21√2, 30, 22√2, 24√2, 30√2, 46, 48, 60, 46√2, 72, 92, 69√2, 104, 75√2, 80√2, 116, 92√2, 104√2.

Code: 1167 0 254 920 116 254 921 208 254 462 254 208 461 254 254 1046 150 104 240 24 162 241 48 162 725 48 90 804 128 82 692 69 69 481 48 138 226 128 82 1045 150 0 214 69 69 156 75 75 307 90 90 300 120 90 750 75 75 601 150 60

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)