Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256AT GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 6, 6√2, 12, 11√2, 12√2, 22, 22√2, 44, 44√2, 64, 53√2, 84, 86, 66√2, 106, 108, 84√2, 86√2, 126, 106√2.

Code: 1065 0 150 1064 106 150 226 190 234 447 212 256 446 212 212 1263 190 108 662 256 168 846 172 84 645 0 86 534 53 97 116 53 97 225 64 86 1081 172 108 122 184 96 121 184 108 62 190 102 61 190 108 867 0 86 860 86 86 845 172 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)