Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:364AP GHM

Order: 20

Horizontal side: 364 Vertical side: 364

Elements: 11√2, 22, 28, 22√2, 24√2, 38, 44, 48, 38√2, 66, 55√2, 96, 77√2, 110, 96√2, 103√2, 158, 134√2, 206, 182√2.

Code: 2065 0 158 1824 182 182 1346 230 230 483 230 182 382 268 192 383 268 154 962 364 96 244 206 158 283 230 154 1585 0 0 1034 103 55 443 202 110 667 202 154 776 191 77 556 103 55 1105 158 0 224 180 88 223 202 88 963 364 0 114 191 77

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)