Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:217AA GHM

Order: 20

Horizontal side: 217 Vertical side: 217

Elements: 8, 24, 32, 24√2, 34, 40, 44, 32√2, 48, 34√2, 39√2, 40√2, 61, 44√2, 78, 56√2, 61√2, 78√2, 122, 139.

Code: 1397 0 217 440 139 217 441 183 217 342 217 183 341 217 217 1223 217 61 566 39 117 325 95 141 324 127 141 240 159 173 241 183 173 83 135 141 487 135 149 402 135 101 401 135 141 390 39 117 787 0 78 780 78 78 614 156 0 613 217 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)