Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:328AE2of2 GHM

Order: 20

Horizontal side: 328 Vertical side: 328

Elements: 14√2, 16√2, 28, 32, 24√2, 40, 32√2, 48, 56, 42√2, 64, 72, 56√2, 61√2, 122, 89√2, 150, 178, 136√2, 164√2.

Code: 1785 0 150 1644 164 164 1366 192 192 283 192 164 725 192 120 144 178 150 426 150 122 1505 0 0 894 89 61 616 89 61 1225 150 0 407 192 120 166 216 104 327 232 120 326 232 88 645 264 56 246 192 80 485 216 56 564 272 0 563 328 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)