Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:189AA GHM

Order: 20

Horizontal side: 189 Vertical side: 189

Elements: 1√2, 22, 28, 23√2, 34, 28√2, 45, 46, 47, 48, 34√2, 62, 45√2, 47√2, 48√2, 71, 73, 94, 96, 71√2.

Code: 715 0 118 714 71 118 470 142 189 471 189 189 236 72 119 465 95 96 941 189 142 10 72 119 737 0 118 286 45 90 225 73 96 345 73 62 344 107 62 963 141 0 482 189 48 456 0 45 285 45 62 627 45 62 483 189 0 455 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)