Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:185AB GHM

Order: 20

Horizontal side: 185 Vertical side: 185

Elements: 5, 5√2, 16√2, 32, 35, 39, 30√2, 32√2, 46, 35√2, 50, 39√2, 64, 65, 70, 50√2, 71, 75, 100, 75√2.

Code: 755 0 110 754 75 110 703 150 115 352 185 150 351 185 185 1003 185 50 50 80 115 51 85 115 657 85 115 397 0 110 396 0 71 467 39 110 306 55 80 160 55 80 715 0 0 327 39 64 326 39 32 645 71 0 504 135 0 503 185 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)