Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234AW GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 2√2, 12, 12√2, 24, 18√2, 23√2, 25√2, 36, 46, 50, 36√2, 54, 46√2, 84, 92, 94, 96, 94√2, 138, 140.

Code: 1405 0 94 1381 138 234 845 138 150 961 234 234 545 138 96 364 174 114 363 210 114 127 210 150 120 222 150 247 210 138 923 234 46 184 192 96 24 140 94 256 117 71 507 142 96 947 0 94 940 94 94 234 117 71 464 188 0 463 234 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)