Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256BG GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 4, 4√2, 8, 12, 9√2, 14, 18, 14√2, 32, 23√2, 41√2, 58, 70, 58√2, 70√2, 116, 128, 93√2, 140, 128√2.

Code: 1405 0 116 1284 128 128 1283 256 128 121 140 128 85 140 120 584 198 70 583 256 70 45 140 116 44 144 116 183 148 102 92 157 111 1167 0 116 236 93 93 145 116 102 144 130 102 410 157 111 327 116 102 930 93 93 704 186 0 703 256 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)