Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186AR GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 2, 2√2, 4, 3√2, 4√2, 14√2, 36, 32√2, 50, 36√2, 54, 40√2, 64, 50√2, 72, 54√2, 78, 82, 100, 75√2.

Code: 785 0 108 754 75 111 723 150 114 362 186 150 361 186 186 1003 186 50 36 75 111 45 78 110 44 82 110 326 54 82 647 86 114 25 78 108 24 80 108 542 54 54 404 40 68 146 40 68 825 54 0 543 54 0 504 136 0 503 186 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)