Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:189AB 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, 70, 72, 94, 96, 72√2.

Code: 725 0 117 724 72 117 450 144 189 451 189 189 280 99 144 281 127 144 627 127 144 963 189 48 707 0 117 230 70 117 14 71 116 221 93 116 342 127 82 341 127 116 476 0 47 945 47 0 461 93 94 484 141 0 483 189 0 475 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)