Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:190AG GHM

Order: 20

Horizontal side: 190 Vertical side: 190

Elements: 5√2, 6√2, 10, 28, 34, 26√2, 40, 34√2, 36√2, 40√2, 60, 62, 48√2, 68, 70, 54√2, 80, 82, 60√2, 75√2.

Code: 827 0 190 480 82 190 544 136 136 606 130 130 340 34 142 341 68 142 627 68 142 366 94 106 62 136 136 605 130 70 687 0 108 283 68 80 260 94 106 406 0 40 807 40 80 56 115 75 105 120 70 750 115 75 701 190 70 405 0 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)