Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:177AD GHM

Order: 20

Horizontal side: 177 Vertical side: 177

Elements: 5√2, 14, 11√2, 22, 19√2, 22√2, 33, 38, 43, 44, 48, 52, 43√2, 62, 66, 48√2, 72, 86, 96, 72√2.

Code: 725 0 105 724 72 105 110 144 177 331 177 177 663 133 100 227 133 166 220 155 166 447 133 144 963 177 48 627 0 105 190 62 105 54 67 100 141 81 100 527 81 100 436 0 43 865 43 0 381 81 86 484 129 0 483 177 0 435 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)