Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AT GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 16√2, 18√2, 32, 24√2, 36, 40, 32√2, 48, 36√2, 37√2, 50√2, 74, 54√2, 61√2, 98, 74√2, 122, 98√2, 148, 172.

Code: 1725 0 98 1481 148 270 542 202 216 1221 270 270 180 202 216 360 184 198 361 220 198 502 270 148 407 148 162 166 172 146 327 188 162 326 188 130 746 196 74 246 148 122 485 172 98 987 0 98 980 98 98 614 159 37 376 159 37 745 196 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)