Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:341AF GHM

Order: 20

Horizontal side: 341 Vertical side: 341

Elements: 12, 12√2, 24, 18√2, 24√2, 48, 55, 55√2, 81, 88, 66√2, 110, 81√2, 117, 132, 143, 150, 110√2, 176, 143√2.

Code: 1767 0 341 1100 176 341 1101 286 341 552 341 286 551 341 341 1436 198 143 666 0 165 1327 66 231 1503 198 81 887 198 231 485 0 117 1435 198 0 1175 0 0 244 24 93 243 48 93 182 66 99 124 36 81 123 48 81 814 117 0 813 198 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)